Numerical Methods for Partial Differential Equations

Article	Citations
A wavelet based numerical scheme for fractional order SEIR epidemic of measles by using Genocchi polynomials	139
A study on fractional host–parasitoid population dynamical model to describe insect species	75
The reducing rank method to solve third‐order Duffing equation with the homotopy perturbation	73
New numerical simulation for fractional Benney–Lin equation arising in falling film problems using two novel techniques	70
Numerical investigations on COVID‐19 model through singular and non‐singular fractional operators	66
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 temperature	64
He's frequency formulation for fractal nonlinear oscillator arising in a microgravity space	64
Analytical and numerical approaches to nerve impulse model of fractional‐order	57
A mathematical analysis of ongoing outbreakCOVID‐19 in India through nonsingular derivative	55
A generalized differential quadrature algorithm for simulating magnetohydrodynamic peristaltic flow of blood‐based nanofluid containing magnetite nanoparticles: A physiological application	55
Results on approximate controllability results for second‐order Sobolev‐type impulsive neutral differential evolution inclusions with infinite delay	54
Microorganisms swimming through radiative Sutterby nanofluid over stretchable cylinder: Hydrodynamic effect	53
An efficient computational approach for local fractional Poisson equation in fractal media	52
Emphasis on unsteady dynamics of bioconvective hybrid nanofluid flow over an upward–downward moving rotating disk	46
A new study on existence and uniqueness of nonlocal fractional delay differential systems of order 1 < r < 2 in Banach spaces	46
European option pricing models described by fractional operators with classical and generalizedMittag‐Lefflerkernels	45
A new exploration on existence of Sobolev‐type Hilfer fractional neutral integro‐differential equations with infinite delay	45
Boundary layer flow pattern of heat and mass for homogenous shear thinning hybrid‐nanofluid: An experimental data base modeling	45
An efficient numerical approach for fractional multidimensional diffusion equations with exponential memory	42
Mathematical modeling for novel coronavirus (COVID‐19) and control	39
A fractional model for population dynamics of two interacting species by using spectral and Hermite wavelets methods	39
Numerical solutions for solving model time‐fractionalFokker–Planckequation	38
Mathematical model for spreading of COVID‐19 virus with the Mittag–Leffler kernel	37
Generalized differential quadrature scrutinization of an advanced MHD stability problem concerned water‐based nanofluids with metal/metal oxide nanomaterials: A prop	35
Implicit meshless method to solve 2D fractional stochastic Tricomi‐type equation defined on irregular domain occurring in fractal transonic flow	34

Linear barycentric rational collocation method for solving heat conduction equation	34
New discussion on approximate controllability results for fractional Sobolev type Volterra‐Fredholm integro‐differential systems of order 1 < r < 2	34
A novel numerical manner for two‐dimensional space fractional diffusion equation arising in transport phenomena	33
Existence and controllability of nonlocal mixed Volterra‐Fredholm type fractional delay integro‐differential equations of order 1 < r < 2	33
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 an	31
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 a	31
Heat and mass transfer analysis for bioconvective flow of Eyring Powell nanofluid over a Riga surface with nonlinear thermal features	31
Legendre wavelet collocation method for fractional optimal control problems with fractional Bolza cost	29
Numerical solutions of distributed order fractional differential equations in the time domain using the Müntz–Legendre wavelets approach	28
Integrated neuro‐evolution heuristic with sequential quadratic programming for second‐order prediction differential models	26
Numerical study and chaotic oscillations for aerodynamic model of wind turbine via fractal and fractional differential operators	26
New results concerning to approximate controllability of Hilfer fractional neutral stochastic delay integro‐differential systems	26
Computational investigation of heat transfer in a flow subjected to magnetohydrodynamic of Maxwell nanofluid over a stretched flat sheet with thermal radiation	25
Numerical approach to chaotic pattern formation in diffusive predator–prey system with Caputo fractional operator	25
A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions	25
A study over the general formula of regression sum of squares in multiple linear regression	25
An efficient computational technique for time‐fractionalKaup‐Kupershmidtequation	24
Controlled fuzzy metric spaces and some related fixed point results	23
Computational examination of Casson nanofluid due to a non‐linear stretching sheet subjected to particle shape factor: Tiwari and Das model	23
An efficient tool for solving two‐dimensional fuzzy fractional‐ordered heat equation	23
A robust scheme based on novel‐operational matrices for some classes of time‐fractional nonlinear problems arising in mechanics and mathematical physics	22
On the nondifferentiable exact solutions to Schamel's equation with local fractional derivative on Cantor sets	22
Finite difference/collocation method to solve multi term variable‐order fractional reaction–advection–diffusion equation in heterogeneous medium	22
Numerical and theoretical discussions for solving nonlinear generalized Benjamin–Bona–Mahony–Burgers equation based on the Legendre spectral element method	22
Numerical and mathematical analysis of induction motor by means of AB–fractal–fractional differentiation actuated by drilling system	20
A reduced‐order modified finite difference method preserving unconditional energy‐stability for the Allen–Cahn equation	20
A stable computational approach to analyze semi‐relativistic behavior of fractional evolutionary problems	20
Modeling and numerical investigation of fractional‐order bovine babesiosis disease	20
A local hybrid kernel meshless method for numerical solutions of two‐dimensional fractional cable equation in neuronal dynamics	20
Long time error analysis of the fourth‐order compact finite difference methods for the nonlinear Klein–Gordon equation with weak nonlinearity	19
Mathematical modeling of bio‐magnetic fluid bounded within ciliated walls of wavy channel	19
Computational analysis of the third order dispersive fractional PDE under exponential‐decay and Mittag‐Leffler type kernels	19
A fast implicit difference scheme for solving the generalized time–space fractional diffusion equations with variable coefficients	19
Weighted Hermite–Hadamard–Mercer type inequalities for convex functions	19
Jacobi collocation method for the fractional advection‐dispersion equation arising in porous media	18
Barycentric rational interpolation and local radial basis functions based numerical algorithms for multidimensional sine‐Gordon equation	18
Barycentric rational method for solving biharmonic equation by depression of order	18
A two‐grid method with backtracking for the mixed Navier–Stokes/Darcy model	18
A stabilizer free weak Galerkin finite element method with supercloseness of order two	18
Comparison between the new exact and numerical solutions of the Mikhailov–Novikov–Wang equation	17
A high order numerical scheme for solving a class of non‐homogeneous time‐fractional reaction diffusion equation	17
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 exponential	17
A reduced‐order extrapolating space–time continuous finite element method for the 2D Sobolev equation	17
Effects of radiative heat flux and heat generation on magnetohydodynamics natural convection flow of nanofluid inside a porous triangular cavity with thermal boundary conditions	17
A Haar wavelet collocation approach for solving one and two‐dimensional second‐order linear and nonlinear hyperbolic telegraph equations	17
Analysis of a momentum conservative mixed‐FEM for the stationary Navier–Stokes problem	17
New formulas of the high‐order derivatives of fifth‐kind Chebyshev polynomials: Spectral solution of the convection–diffusion equation	17
A new and efficient numerical method based on shifted fractional‐order Jacobi operational matrices for solving some classes of two‐dimensional nonlinear fractional integral equations	17
Numerical solutions of the equal width equation by trigonometric cubic B‐spline collocation method based on Rubin–Graves type linearization	16
New results concerning to approximate controllability of fractional integro‐differential evolution equations of order 1 < r < 2	16

Investigation of Coriolis effect on oceanic flows and its bifurcation via geophysical Korteweg–de Vries equation	16
Results on approximate controllability of Sobolev type fractional stochastic evolution hemivariational inequalities	16
The fast scalar auxiliary variable approach with unconditional energy stability for nonlocal Cahn–Hilliard equation	16
Construction and analysis of some nonstandard finite difference methods for the FitzHugh–Nagumo equation	16
A class of new stable, explicit methods to solve the non‐stationary heat equation	16
A new approach by two‐dimensional wavelets operational matrix method for solving variable‐order fractional partial integro‐differential equations	15
Results on existence and controllability results for fractional evolution inclusions of order 1 < r < 2 with Clarke's subdifferential type	15
A parameter‐uniform scheme for the parabolic singularly perturbed problem with a delay in time	15
Dual fractional modeling of rate type fluid through non‐local differentiation	15
A study on fractional predator–prey–pathogen model with Mittag–Leffler kernel‐based operators	15
On solution of a class of nonlinear variable order fractional reaction–diffusion equation with Mittag–Leffler kernel	15
Linearized stable spectral method to analyze two‐dimensional nonlinear evolutionary and reaction‐diffusion models	14
An improvised collocation algorithm with specific end conditions for solving modified Burgers equation	14
The pointwise estimates of a conservative difference scheme for Burgers' equation	14
An inverse problem of identifying the time‐dependent potential in a fourth‐order pseudo‐parabolic equation from additional condition	14
Approximate controllability results for Sobolev‐type delay differential system of fractional order without uniqueness	14
Finite difference method combined with differential quadrature method for numerical computation of the modified equal width wave equation	13
A new high‐order weighted essentially non‐oscillatory scheme for non‐linear degenerate parabolic equations	13
Numerical solution of fractional partial differential equations via Haar wavelet	13
Simple and efficient continuous data assimilation of evolution equations via algebraic nudging	13
Novel applications of the magnetohydrodynamics couple stress fluid flows between two plates with fractal‐fractional derivatives	13
Soret–Dufour mechanism on an electrically conducting nanofluid flow past a semi‐infinite porous plate with buoyancy force and chemical reaction influence	12
Decatic B‐spline collocation scheme for approximate solution of Burgers' equation	12
On the absolute stable difference scheme for the space‐wise dependent source identification problem for elliptic‐telegraph equation	12
High‐order finite difference/spectral‐Galerkin approximations for the nonlinear time–space fractional Ginzburg–Landau equation	12
Results on approximate controllability of neutral integro‐differential stochastic system with state‐dependent delay	12
Analytical and numerical solutions of the Fitzhugh–Nagumo equation and their multistability behavior	12
Half‐inverse problems for the quadratic pencil of the Sturm–Liouville equations with impulse	11
On Romanovski–Jacobi polynomials and their related approximation results	11
Combination of Shehu decomposition and variational iteration transform methods for solving fractional third order dispersive partial differential equations	11
Weak Galerkin finite element method for a class of time fractional generalized Burgers' equation	11
New extensions of Hermite–Hadamard inequalities via generalized proportional fractional integral	11
On refinements of some integral inequalities using improved power‐mean integral inequalities	11
Optimal uniform error estimates for moving least‐squares collocation with application to option pricing under jump‐diffusion processes	11
Approximation of functions by a new construction of Bernstein‐Chlodowsky operators: Theory and applications	10
Heat transfer analysis on MHD flow over a stretchable Riga wall considering Entropy generation rate: A numerical study	10
Influence of thermophoretic diffusion of nanoparticles with Joule heating in flow of Maxwell nanofluid	10
An unconditionally stable algorithm for multiterm time fractional advection–diffusion equation with variable coefficients and convergence analysis	10
Numerical simulation and modeling of entropy generation in Marangoni convective flow of nanofluid with activation energy	10
Learning parameters of a system of variable order fractional differential equations	10
Convergence analysis of the fractional decomposition method with applications to time‐fractional biological population models	9
Single soliton and double soliton solutions of the quadratic‐nonlinear Korteweg‐de Vries equation for small and long‐times	9
CVFEM based numerical investigation and mathematical modeling of surface dependent magnetized copper‐oxide nanofluid flow using new model of porous space	9
Numerical approximation of a stochastic age‐structured population model in a polluted environment with Markovian switching	9
Exact solutions of convective–diffusive Cahn–Hilliard equation using extended direct algebraic method	9
Numerical simulation for entropy optimized nonlinear radiative flow of GO‐Al 2 O 3 magneto nanomaterials with auto catalysis chemi	9
Exact solutions of (2 + 1)‐dimensional Schrödinger's hyperbolic equation using different techniques	9
A numerical analysis for fractional model of the spread of pests in tea plants	9
The numerical analysis of two linearized difference schemes for the Benjamin–Bona–Mahony–Burgers equation	9
A fast temporal second‐order difference scheme for the time‐fractional subdiffusion equation	9
A numerical technique based on B‐spline for a class of time‐fractional diffusion equation	9
Cattaneo–Christov heat flux model for three‐dimensional magnetohydrodynamic flow of an Eyring Powell fluid over an exponentially stretching surface with convective boundary condition	9
A high‐order weighted essentially nonoscillatory scheme based on exponential polynomials for nonlinear degenerate parabolic equations	9
Analysis of a novel finance chaotic model via ABC fractional derivative	9
Numerical solution of fuzzy fractional diffusion equation by Chebyshev spectral method	8
Finite difference technique to solve a problem of generalized thermoelasticity on an annular cylinder under the effect of rotation	8
The optimal homotopy analysis method applied on nonlinear time‐fractional hyperbolic partial differential equations	8
On solutions of fuzzy fractional order complex population dynamical model	8
Unconditionally stable exponential time differencing schemes for the mass‐conserving Allen–Cahn equation with nonlocal and local effects	8
Numerical solution of the multiterm time‐fractional diffusion equation based on reproducing kernel theory	8
Simultaneous inversion of two initial values for a time‐fractional diffusion‐wave equation	8
Fully spectral‐Galerkin method for the one‐ and two‐dimensional fourth‐order time‐fractional partial integro‐differential equations with a weakly singular kernel	8
Numerical wavelets scheme to complex partial differential equation arising from Morlet continuous wavelet transform	8
Compact difference scheme for two‐dimensional fourth‐order nonlinear hyperbolic equation	8
A modified Chebyshev ϑ‐weighted Crank–Nicolson method for analyzing fractional sub‐diffusion equations	7
Finite element theory on curved domains with applications to discontinuous Galerkin finite element methods	7
A non‐iterative domain decomposition method for the interaction between a fluid and a thick structure	7
MHD two‐phase flow of Jeffrey fluid suspended with Hafnium and crystal particles: Analytical treatment	7
Dynamics of Arrhenius activation energy in flow of Carreau fluid subject to Brownian motion diffusion	7
Existence and uniqueness of solutions for fractional nonlinear hybrid impulsive system	7
Analysis and efficient implementation of alternating direction implicit finite volume method for Riesz space‐fractional diffusion equations in two space dimensions	7
Convergence analysis of a hp‐finite element approximation of the time‐harmonic Maxwell equations with impedance boundary conditions in domains with an analytic boundary	7
A novel scheme for time‐fractional semi‐relativistic Vlasov–Maxwell system based on laser‐plasma interaction with linear polarization and Landau damping instability	7
An efficient spectral method and rigorous error analysis based on dimension reduction scheme for fourth order problems	7
Fast calculation based on a spatial two‐grid finite element algorithm for a nonlinear space–time fractional diffusion model	7
Second‐order, fully decoupled, linearized, and unconditionally stable scalar auxiliary variable schemes for Cahn–Hilliard–Darcy system	7
Numerical simulation of two‐dimensional and three‐dimensional generalizedKlein–Gordon–Zakharovequations with power law nonlinearity via a meshless collocation method based on barycentric ra	7
Symplectic‐preserving Fourier spectral scheme for space fractionalKlein–Gordon–Schrödingerequations	7
Numerical solutions of generalized Rosenau–KDV–RLW equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization	7
A novel approach for the solution of fractional diffusion problems with conformable derivative	7

Optimal error analysis of Crank–Nicolson lowest‐order Galerkin‐mixed finite element method for incompressible miscible flow in porous media	6
Discontinuous Galerkin method for the coupled Stokes‐Biot model	6
Quadratic B‐spline collocation method for time dependent singularly perturbed differential‐difference equation arising in the modeling of neuronalactivity	6
Numerical solution of singularly perturbed 2D parabolic initial‐boundary‐value problems based on reproducing kernel theory: Error and stability analysis	6
Numerical analysis of a second order ensemble method for evolutionary magnetohydrodynamics equations at small magnetic Reynolds number	6
Numerical solution of fractional Dullin–Gottwald–Holm equation for solitary shallow water waves	6
Accurate and efficient algorithms with unconditional energy stability for the time fractional Cahn–Hilliard and Allen–Cahn equations	6
Results on approximate controllability of nondensely defined fractional neutral stochastic differential systems	6
Weakly symmetric stress equilibration and a posteriori error estimation for linear elasticity	6
On solutions of time‐fractional advection–diffusion equation	6
A second order ensemble method with different subdomain time steps for simulating coupled surface‐groundwater flows	6
A C0 linear finite element method for a second‐order elliptic equation in non‐divergence form with Cordes coefficients	6
Reproducing kernel method to solve parabolic partial differential equations with nonlocal conditions	6
On the dynamics of strong Langmuir turbulence through the five recent numerical schemes in the plasma physics	6
A numerical study on fractional differential equation with population growth model	6
A combined meshfree exponential Rosenbrock integrator for the third‐order dispersive partial differential equations	6