Numerical Methods for Partial Differential Equations

Papers
(The median citation count of Numerical Methods for Partial Differential Equations is 2. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2020-04-01 to 2024-04-01.)
ArticleCitations
A wavelet based numerical scheme for fractional order SEIR epidemic of measles by using Genocchi polynomials146
A study on fractional host–parasitoid population dynamical model to describe insect species86
New numerical simulation for fractional Benney–Lin equation arising in falling film problems using two novel techniques73
The reducing rank method to solve third‐order Duffing equation with the homotopy perturbation73
Numerical investigations on COVID‐19 model through singular and non‐singular fractional operators72
He's frequency formulation for fractal nonlinear oscillator arising in a microgravity space65
Hall and ion slip effects on magnetohydrodynamic convective rotating flow of Jeffreys fluid over an impulsively moving vertical plate embedded in a saturated porous medium with Ramped wall temperature65
Analytical and numerical approaches to nerve impulse model of fractional‐order57
Microorganisms swimming through radiative Sutterby nanofluid over stretchable cylinder: Hydrodynamic effect57
A mathematical analysis of ongoing outbreakCOVID‐19 in India through nonsingular derivative55
A generalized differential quadrature algorithm for simulating magnetohydrodynamic peristaltic flow of blood‐based nanofluid containing magnetite nanoparticles: A physiological application55
Results on approximate controllability results for second‐order Sobolev‐type impulsive neutral differential evolution inclusions with infinite delay54
An efficient computational approach for local fractional Poisson equation in fractal media52
Emphasis on unsteady dynamics of bioconvective hybrid nanofluid flow over an upward–downward moving rotating disk47
European option pricing models described by fractional operators with classical and generalizedMittag‐Lefflerkernels46
A new study on existence and uniqueness of nonlocal fractional delay differential systems of order 1 < r < 2 in Banach spaces46
A new exploration on existence of Sobolev‐type Hilfer fractional neutral integro‐differential equations with infinite delay45
Boundary layer flow pattern of heat and mass for homogenous shear thinning hybrid‐nanofluid: An experimental data base modeling45
An efficient numerical approach for fractional multidimensional diffusion equations with exponential memory42
A fractional model for population dynamics of two interacting species by using spectral and Hermite wavelets methods41
Mathematical modeling for novel coronavirus (COVID‐19) and control39
Numerical solutions for solving model time‐fractionalFokker–Planckequation38
Mathematical model for spreading of COVID‐19 virus with the Mittag–Leffler kernel37
Implicit meshless method to solve 2D fractional stochastic Tricomi‐type equation defined on irregular domain occurring in fractal transonic flow36
Existence and controllability of nonlocal mixed Volterra‐Fredholm type fractional delay integro‐differential equations of order 1 < r < 235
Generalized differential quadrature scrutinization of an advanced MHD stability problem concerned water‐based nanofluids with metal/metal oxide nanomaterials: A prop35
New discussion on approximate controllability results for fractional Sobolev type Volterra‐Fredholm integro‐differential systems of order 1 < r < 235
Heat and mass transfer analysis for bioconvective flow of Eyring Powell nanofluid over a Riga surface with nonlinear thermal features34
Linear barycentric rational collocation method for solving heat conduction equation34
A novel numerical manner for two‐dimensional space fractional diffusion equation arising in transport phenomena33
Numerical solutions of the partial differential equations for investigating the significance of partial slip due to lateral velocity and viscous dissipation: The case of blood‐gold Carreau nanofluid a32
Numerical simulation of a nonlinear coupled differential system describing a convective flow of Casson gold–blood nanofluid through a stretched rotating rigid disk in the presence of Lorentz forces an31
Legendre wavelet collocation method for fractional optimal control problems with fractional Bolza cost30
A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions28
Numerical solutions of distributed order fractional differential equations in the time domain using the Müntz–Legendre wavelets approach28
Integrated neuro‐evolution heuristic with sequential quadratic programming for second‐order prediction differential models26
Numerical study and chaotic oscillations for aerodynamic model of wind turbine via fractal and fractional differential operators26
New results concerning to approximate controllability of Hilfer fractional neutral stochastic delay integro‐differential systems26
Numerical approach to chaotic pattern formation in diffusive predator–prey system with Caputo fractional operator25
Computational investigation of heat transfer in a flow subjected to magnetohydrodynamic of Maxwell nanofluid over a stretched flat sheet with thermal radiation25
A study over the general formula of regression sum of squares in multiple linear regression25
Finite difference/collocation method to solve multi term variable‐order fractional reaction–advection–diffusion equation in heterogeneous medium24
An efficient computational technique for time‐fractionalKaup‐Kupershmidtequation24
Controlled fuzzy metric spaces and some related fixed point results24
On the nondifferentiable exact solutions to Schamel's equation with local fractional derivative on Cantor sets23
Computational examination of Casson nanofluid due to a non‐linear stretching sheet subjected to particle shape factor: Tiwari and Das model23
Numerical and theoretical discussions for solving nonlinear generalized Benjamin–Bona–Mahony–Burgers equation based on the Legendre spectral element method23
An efficient tool for solving two‐dimensional fuzzy fractional‐ordered heat equation23
A robust scheme based on novel‐operational matrices for some classes of time‐fractional nonlinear problems arising in mechanics and mathematical physics22
Computational analysis of the third order dispersive fractional PDE under exponential‐decay and Mittag‐Leffler type kernels21
Modeling and numerical investigation of fractional‐order bovine babesiosis disease20
A fast implicit difference scheme for solving the generalized time–space fractional diffusion equations with variable coefficients20
A stable computational approach to analyze semi‐relativistic behavior of fractional evolutionary problems20
Weighted Hermite–Hadamard–Mercer type inequalities for convex functions20
A local hybrid kernel meshless method for numerical solutions of two‐dimensional fractional cable equation in neuronal dynamics20
Numerical and mathematical analysis of induction motor by means of AB–fractal–fractional differentiation actuated by drilling system20
A reduced‐order modified finite difference method preserving unconditional energy‐stability for the Allen–Cahn equation20
Mathematical modeling of bio‐magnetic fluid bounded within ciliated walls of wavy channel19
Analysis of a momentum conservative mixed‐FEM for the stationary Navier–Stokes problem19
Long time error analysis of the fourth‐order compact finite difference methods for the nonlinear Klein–Gordon equation with weak nonlinearity19
A high order numerical scheme for solving a class of non‐homogeneous time‐fractional reaction diffusion equation18
A Haar wavelet collocation approach for solving one and two‐dimensional second‐order linear and nonlinear hyperbolic telegraph equations18
A two‐grid method with backtracking for the mixed Navier–Stokes/Darcy model18
Comparison between the new exact and numerical solutions of the Mikhailov–Novikov–Wang equation18
Investigation of Coriolis effect on oceanic flows and its bifurcation via geophysical Korteweg–de Vries equation18
Construction and analysis of some nonstandard finite difference methods for the FitzHugh–Nagumo equation18
Jacobi collocation method for the fractional advection‐dispersion equation arising in porous media18
A stabilizer free weak Galerkin finite element method with supercloseness of order two18
A study on fractional predator–prey–pathogen model with Mittag–Leffler kernel‐based operators18
Barycentric rational interpolation and local radial basis functions based numerical algorithms for multidimensional sine‐Gordon equation18
A formally second‐order backward differentiation formula Sinc‐collocation method for the Volterra integro‐differential equation with a weakly singular kernel based on the double exponential18
Barycentric rational method for solving biharmonic equation by depression of order18
A reduced‐order extrapolating space–time continuous finite element method for the 2D Sobolev equation17
The fast scalar auxiliary variable approach with unconditional energy stability for nonlocal Cahn–Hilliard equation17
A new and efficient numerical method based on shifted fractional‐order Jacobi operational matrices for solving some classes of two‐dimensional nonlinear fractional integral equations17
New formulas of the high‐order derivatives of fifth‐kind Chebyshev polynomials: Spectral solution of the convection–diffusion equation17
Results on existence and controllability results for fractional evolution inclusions of order 1 < r < 2 with Clarke's subdifferential type16
Dual fractional modeling of rate type fluid through non‐local differentiation16
Numerical solutions of the equal width equation by trigonometric cubic B‐spline collocation method based on Rubin–Graves type linearization16
New results concerning to approximate controllability of fractional integro‐differential evolution equations of order 1 < r < 216
Effects of radiative heat flux and heat generation on magnetohydodynamics natural convection flow of nanofluid inside a porous triangular cavity with thermal boundary conditions16
A class of new stable, explicit methods to solve the non‐stationary heat equation16
A parameter‐uniform scheme for the parabolic singularly perturbed problem with a delay in time15
Results on approximate controllability of Sobolev type fractional stochastic evolution hemivariational inequalities15
Numerical solution of fractional partial differential equations via Haar wavelet15
On solution of a class of nonlinear variable order fractional reaction–diffusion equation with Mittag–Leffler kernel15
A new approach by two‐dimensional wavelets operational matrix method for solving variable‐order fractional partial integro‐differential equations15
The pointwise estimates of a conservative difference scheme for Burgers' equation15
An improvised collocation algorithm with specific end conditions for solving modified Burgers equation14
Simple and efficient continuous data assimilation of evolution equations via algebraic nudging14
An inverse problem of identifying the time‐dependent potential in a fourth‐order pseudo‐parabolic equation from additional condition14
Approximate controllability results for Sobolev‐type delay differential system of fractional order without uniqueness14
Linearized stable spectral method to analyze two‐dimensional nonlinear evolutionary and reaction‐diffusion models14
Finite difference method combined with differential quadrature method for numerical computation of the modified equal width wave equation13
A new high‐order weighted essentially non‐oscillatory scheme for non‐linear degenerate parabolic equations13
Results on approximate controllability of neutral integro‐differential stochastic system with state‐dependent delay13
Analytical and numerical solutions of the Fitzhugh–Nagumo equation and their multistability behavior13
Novel applications of the magnetohydrodynamics couple stress fluid flows between two plates with fractal‐fractional derivatives13
On refinements of some integral inequalities using improved power‐mean integral inequalities12
Soret–Dufour mechanism on an electrically conducting nanofluid flow past a semi‐infinite porous plate with buoyancy force and chemical reaction influence12
Decatic B‐spline collocation scheme for approximate solution of Burgers' equation12
On the absolute stable difference scheme for the space‐wise dependent source identification problem for elliptic‐telegraph equation12
Structure of analytical and symbolic computational approach of multiple solitary wave solutions for nonlinear Zakharov‐Kuznetsov modified equal width equation12
A numerical technique based on B‐spline for a class of time‐fractional diffusion equation11
New extensions of Hermite–Hadamard inequalities via generalized proportional fractional integral11
Weak Galerkin finite element method for a class of time fractional generalized Burgers' equation11
Influence of thermophoretic diffusion of nanoparticles with Joule heating in flow of Maxwell nanofluid11
The numerical analysis of two linearized difference schemes for the Benjamin–Bona–Mahony–Burgers equation11
On Romanovski–Jacobi polynomials and their related approximation results11
Half‐inverse problems for the quadratic pencil of the Sturm–Liouville equations with impulse11
High‐order finite difference/spectral‐Galerkin approximations for the nonlinear time–space fractional Ginzburg–Landau equation11
Optimal uniform error estimates for moving least‐squares collocation with application to option pricing under jump‐diffusion processes11
Approximation of functions by a new construction of Bernstein‐Chlodowsky operators: Theory and applications10
Analysis of a novel finance chaotic model via ABC fractional derivative10
Learning parameters of a system of variable order fractional differential equations10
An unconditionally stable algorithm for multiterm time fractional advection–diffusion equation with variable coefficients and convergence analysis10
Numerical simulation and modeling of entropy generation in Marangoni convective flow of nanofluid with activation energy10
Heat transfer analysis on MHD flow over a stretchable Riga wall considering Entropy generation rate: A numerical study10
A fast temporal second‐order difference scheme for the time‐fractional subdiffusion equation10
Exact solutions of (2 + 1)‐dimensional Schrödinger's hyperbolic equation using different techniques9
CVFEM based numerical investigation and mathematical modeling of surface dependent magnetized copper‐oxide nanofluid flow using new model of porous space9
Numerical approximation of a stochastic age‐structured population model in a polluted environment with Markovian switching9
Simultaneous inversion of two initial values for a time‐fractional diffusion‐wave equation9
Cattaneo–Christov heat flux model for three‐dimensional magnetohydrodynamic flow of an Eyring Powell fluid over an exponentially stretching surface with convective boundary condition9
A high‐order weighted essentially nonoscillatory scheme based on exponential polynomials for nonlinear degenerate parabolic equations9
Exact solutions of convective–diffusive Cahn–Hilliard equation using extended direct algebraic method9
Convergence analysis of the fractional decomposition method with applications to time‐fractional biological population models9
Single soliton and double soliton solutions of the quadratic‐nonlinear Korteweg‐de Vries equation for small and long‐times9
Combination of Shehu decomposition and variational iteration transform methods for solving fractional third order dispersive partial differential equations9
A numerical analysis for fractional model of the spread of pests in tea plants9
Numerical simulation for entropy optimized nonlinear radiative flow of GO‐Al 2 O 3 magneto nanomaterials with auto catalysis chemi9
The optimal homotopy analysis method applied on nonlinear time‐fractional hyperbolic partial differential equations8
Fully spectral‐Galerkin method for the one‐ and two‐dimensional fourth‐order time‐fractional partial integro‐differential equations with a weakly singular kernel8
Unconditionally stable exponential time differencing schemes for the mass‐conserving AllenCahn equation with nonlocal and local effects8
Numerical solution of the multiterm time‐fractional diffusion equation based on reproducing kernel theory8
The divergence‐free nonconforming virtual element method for the Navier–Stokes problem8
Numerical solution of fuzzy fractional diffusion equation by Chebyshev spectral method8
Numerical wavelets scheme to complex partial differential equation arising from Morlet continuous wavelet transform8
Compact difference scheme for two‐dimensional fourth‐order nonlinear hyperbolic equation8
On solutions of fuzzy fractional order complex population dynamical model8
A novel approach for the solution of fractional diffusion problems with conformable derivative8
Finite difference technique to solve a problem of generalized thermoelasticity on an annular cylinder under the effect of rotation8
Numerical solution of the partial differential equations that model the steady three‐dimensional flow and heat transfer of Carreau fluid between two stretchable rotatory disks7
Reproducing kernel method to solve parabolic partial differential equations with nonlocal conditions7
Analysis and efficient implementation of alternating direction implicit finite volume method for Riesz space‐fractional diffusion equations in two space dimensions7
Convergence analysis of a hp‐finite element approximation of the time‐harmonic Maxwell equations with impedance boundary conditions in domains with an analytic boundary7
A novel scheme for time‐fractional semi‐relativistic Vlasov–Maxwell system based on laser‐plasma interaction with linear polarization and Landau damping instability7
Thermal instability of magnetohydrodynamic couple stress nanofluid in rotating porous medium7
Numerical solutions of generalized Rosenau–KDV–RLW equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization7
A C0 linear finite element method for a second‐order elliptic equation in non‐divergence form with Cordes coefficients7
Existence and uniqueness of solutions for fractional nonlinear hybrid impulsive system7
Fast calculation based on a spatial two‐grid finite element algorithm for a nonlinear space–time fractional diffusion model7
Finite element theory on curved domains with applications to discontinuous Galerkin finite element methods7
Numerical simulation of two‐dimensional and three‐dimensional generalizedKlein–Gordon–Zakharovequations with power law nonlinearity via a meshless collocation method based on barycentric ra7
MHD two‐phase flow of Jeffrey fluid suspended with Hafnium and crystal particles: Analytical treatment7
Dynamics of Arrhenius activation energy in flow of Carreau fluid subject to Brownian motion diffusion7
An efficient spectral method and rigorous error analysis based on dimension reduction scheme for fourth order problems7
A modified Chebyshev ϑ‐weighted Crank–Nicolson method for analyzing fractional sub‐diffusion equations7
Second‐order, fully decoupled, linearized, and unconditionally stable scalar auxiliary variable schemes for Cahn–Hilliard–Darcy system7
A non‐iterative domain decomposition method for the interaction between a fluid and a thick structure7
Symplectic‐preserving Fourier spectral scheme for space fractionalKlein–Gordon–Schrödingerequations7
A combined meshfree exponential Rosenbrock integrator for the third‐order dispersive partial differential equations6
Numerical analysis of a second order ensemble method for evolutionary magnetohydrodynamics equations at small magnetic Reynolds number6
Optimal error analysis of Crank–Nicolson lowest‐order Galerkin‐mixed finite element method for incompressible miscible flow in porous media6
Results on approximate controllability of nondensely defined fractional neutral stochastic differential systems6
Quadratic B‐spline collocation method for time dependent singularly perturbed differential‐difference equation arising in the modeling of neuronalactivity6
Numerical solution of singularly perturbed 2D parabolic initial‐boundary‐value problems based on reproducing kernel theory: Error and stability analysis6
Unconditionally optimal error estimates of BDF2 Galerkin method for semilinear parabolic equation6
Numerical solution of fractional Dullin–Gottwald–Holm equation for solitary shallow water waves6
Discontinuous Galerkin method for the coupled Stokes‐Biot model6
Perturbation based analytical solutions of non‐Newtonian differential equation with heat and mass transportation between horizontal permeable channel6
Weakly symmetric stress equilibration and a posteriori error estimation for linear elasticity6
On solutions of time‐fractional advection–diffusion equation6
A second order ensemble method with different subdomain time steps for simulating coupled surface‐groundwater flows6
Accurate and efficient algorithms with unconditional energy stability for the time fractional Cahn–Hilliard and Allen–Cahn equations6
Pattern selection in the Schnakenberg equations: From normal to anomalous diffusion6
On the dynamics of strong Langmuir turbulence through the five recent numerical schemes in the plasma physics6
A numerical study on fractional differential equation with population growth model6
A modified walk‐on‐sphere method for high dimensional fractional Poisson equation5
Convergence of a finite element method on a Bakhvalov‐type mesh for a singularly perturbed convection–diffusion equation in 2D5
A hybrid radial basis functions collocation technique to numerically solve fractional advection–diffusion models5
A new approximation for the generalized fractional derivative and its application to generalized fractional diffusion equation5
A second order convergent difference scheme for the initial‐boundary value problem of Korteweg–de Vires equation5
A numerical algorithm for the nonlinear Timoshenko beam system5
Numerical solution of ABC space–time fractional distributed order reaction–diffusion equation5
Uniformly convergent scheme for two‐parameter singularly perturbed problems with non‐smooth data5
A higher‐order hybrid spline difference method on adaptive mesh for solving singularly perturbed parabolic reaction–diffusion problems with robin‐boundary conditions5
Numerical solutions of Boussinesq equation using Galerkin finite element method5
A kernel‐based pseudo‐spectral method for multi‐term and distributed order time‐fractional diffusion equations5
Linearized and decoupled structure‐preserving finite difference methods and their analyses for the coupled SchrödingerBoussinesq equations5
On the numerical solution of conformable fractional diffusion problem with small delay5
A fractional model for anomalous diffusion with increased variability: Analysis, algorithms and applications to interface problems5
A robust multigrid method for one dimensional immersed finite element method5
Local and parallel finite element methods based on two‐grid discretizations for unsteady convection–diffusion problem5
A systematic study on weak Galerkin finite element method for second‐order parabolic problems5
Sharp estimates of the unique solution for two‐point fractional boundary value problems with conformable derivative5
A new stable finite difference scheme and its error analysis for two‐dimensional singularly perturbed convection–diffusion equations5
An effective relaxed alternating procedure for Cauchy problem connected with Helmholtz Equation5
Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow5
Approximation of functions by a new type of Gamma operators5
Partial differential integral equation model for pricing American option under multi state regime switching with jumps5
Haar‐wavelet based approximation for pricing American options under linear complementarity formulations5
On n‐dimensional quadratic B‐splines5
On the L convergence of a conservative Fourier pseudo‐spectral method for the space fractional nonlinear Schrödinger equation5
A fast numerical solution of the 3D nonlinear tempered fractional integrodifferential equation5
Finite element analysis of the singularly perturbed parabolic reaction‐diffusion problems with retarded argument5
An adaptive weak Galerkin finite element method with hierarchical bases for the elliptic problem4
A decoupled stabilized finite element method for the dual‐porosity‐Navier–Stokes fluid flow model arising in shale oil4
Applying the three‐dimensional block‐pulse functions to solve system of Volterra–Hammerstein integral equations4
A kernel‐based method for solving the time‐fractional diffusion equation4
A new convergence and positivity analysis of balanced Euler method for stochastic age‐dependent population equations4
A structure‐preserving finite element approximation of surface diffusion for curve networks and surface clusters4
A new ϕ‐FEM approach for problems with natural boundary conditions4
Numerical solution ofq‐dynamic equations4
Numerical solutions of fractional parabolic equations with generalized Mittag–Leffler kernels4
Numerical analysis for a class of coupled system of singularly perturbed time‐dependent convection‐diffusion equations with a discontinuous source term4
Finite element method with the total stress variable for Biot's consolidation model4
Nonconforming finite element method for coupled Poisson–Nernst–Planck equations4
Assessment of boundary layer for flow of non‐Newtonian material induced by a moving belt with power law viscosity and thermal conductivity models4
A new approach for the qualitative study of vector born disease using Caputo–Fabrizio derivative4
Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation4
An efficient numerical approach to solve a class of variable‐order fractional integro‐partial differential equations4
Linearized compact difference methods for solving nonlinear Sobolev equations with distributed delay4
RBF‐ENO/WENO schemes with Lax–Wendroff type time discretizations for Hamilton–Jacobi equations4
Analysis and numerical simulation of cross reaction–diffusion systems with the Caputo–Fabrizio and Riesz operators4
Convergence analysis of a fast second‐order time‐stepping numerical method for two‐dimensional nonlinear time–space fractional Schrödinger equation4
Convective thermal conditions and the thermophoretic effect's impacts on a hybrid nanofluid over a moving thin needle4
Exponential collocation methods based on continuous finite element approximations for efficiently solving the cubic Schrödinger equation4
An observation on the uniform preconditioners for the mixed Darcy problem4
Dual nature solutions for temperature‐dependent transport properties of nanofluid flow with entropy generation4
On two‐dimensional weakly singular fractional partial integro‐differential equations and dual Bernstein polynomials4
Numerical solutions of the initial boundary value problem for the perturbed conformable time Korteweg‐de Vries equation by using the finite element method4
A new semi‐analytic solution of fractional sixth orderDrinfeld–Sokolov–Satsuma–Hirotaequation4
Finite difference schemes for the fourth‐order parabolic equations with different boundary value conditions4
The analytical solution of fractional‐order Whitham–Broer–Kaup equations by an Elzaki decomposition method4
Conservative unconditionally stable decoupled numerical schemes for the Cahn–Hilliard–Navier–Stokes–Darcy–Boussinesq system3
Superconvergence analysis of a nonconforming finite element method for monotone semilinear elliptic optimal control problems3
Structure‐preserving exponential wave integrator methods and the long‐time convergence analysis for the Klein‐Gordon‐Dirac equation with the small coupling constant3
A multipoint stress mixed finite element method for elasticity on quadrilateral grids3
Application of direct meshless local Petrov–Galerkin method for numerical solution of stochastic elliptic interface problems3
Error estimate on the tanh meshes for the time fractional diffusion equation3
Fourth‐order compact scheme based on quasi‐variable mesh for three‐dimensional mildly nonlinear stationary convection–diffusion equations3
A study of distributed‐order time fractional diffusion models with continuous distribution weight functions3
Block preconditioners for energy stable schemes of magnetohydrodynamics equations3
A fractional system of Cauchy‐reaction diffusion equations by adopting Robotnov function3
A simplified two‐level subgrid stabilized method with backtracking technique for incompressible flows at high Reynolds numbers3
On numerical study of constrained coupled shape optimization problems based on a new shape derivative method3
Mixed convection of ferrofluids in a square enclosure with obstacles: Effect of iso‐perimetric shapes3
Optimal error estimates of fourth‐order compact finite difference methods for the nonlinear Klein–Gordon equation in the nonrelativistic regime3
The element‐free Galerkin method for a quasistatic contact problem with the Tresca friction in elastic materials3
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