Numerical Methods for Partial Differential Equations

Article	Citations
A study on fractional host–parasitoid population dynamical model to describe insect species	102
Numerical investigations onCOVID‐19 model through singular and non‐singular fractional operators	91
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	78
Microorganisms swimming through radiative Sutterby nanofluid over stretchable cylinder: Hydrodynamic effect	64
An efficient computational approach for local fractional Poisson equation in fractal media	57
Emphasis on unsteady dynamics of bioconvective hybrid nanofluid flow over an upward–downward moving rotating disk	54
A generalized differential quadrature algorithm for simulating magnetohydrodynamic peristaltic flow of blood‐based nanofluid containing magnetite nanoparticles: A physiological application	53
Boundary layer flow pattern of heat and mass for homogenous shear thinning hybrid‐nanofluid: An experimental data base modeling	49
European option pricing models described by fractional operators with classical and generalizedMittag‐Lefflerkernels	49
Mathematical model for spreading of COVID‐19 virus with the Mittag–Leffler kernel	48
An efficient numerical approach for fractional multidimensional diffusion equations with exponential memory	44
Mathematical modeling for novel coronavirus (COVID‐19) and control	43
Heat and mass transfer analysis for bioconvective flow of Eyring Powell nanofluid over a Riga surface with nonlinear thermal features	38
Existence and controllability of nonlocal mixedVolterra‐Fredholmtype fractional delay integro‐differential equations of order 1 < r < 2	37
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	37
Legendre wavelet collocation method for fractional optimal control problems with fractional Bolza cost	37
Generalized differential quadrature scrutinization of an advanced MHD stability problem concerned water‐based nanofluids with metal/metal oxide nanomaterials: A prop	35
A novel numerical manner for two‐dimensional space fractional diffusion equation arising in transport phenomena	35
New discussion on approximate controllability results for fractional Sobolev type Volterra‐Fredholm integro‐differential systems of order 1 < r < 2	34
Computational investigation of heat transfer in a flow subjected to magnetohydrodynamic of Maxwell nanofluid over a stretched flat sheet with thermal radiation	33
Modeling and numerical investigation of fractional‐order bovine babesiosis disease	32
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	32
A study on fractional predator–prey–pathogen model with Mittag–Leffler kernel‐based operators	31
A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions	30
Integrated neuro‐evolution heuristic with sequential quadratic programming for second‐order prediction differential models	30

On the nondifferentiable exact solutions to Schamel's equation with local fractional derivative on Cantor sets	28
Computational examination of Casson nanofluid due to a non‐linear stretching sheet subjected to particle shape factor: Tiwari and Das model	28
Barycentric rational interpolation and local radial basis functions based numerical algorithms for multidimensional sine‐Gordon equation	27
Finite difference/collocation method to solve multi term variable‐order fractional reaction–advection–diffusion equation in heterogeneous medium	26
Analysis of a momentum conservative mixed‐FEM for the stationary Navier–Stokes problem	26
Structure of analytical and symbolic computational approach of multiple solitary wave solutions for nonlinear Zakharov‐Kuznetsov modified equal width equation	24
Effects of radiative heat flux and heat generation on magnetohydodynamics natural convection flow of nanofluid inside a porous triangular cavity with thermal boundary conditions	23
Comparison between the new exact and numerical solutions of the Mikhailov–Novikov–Wang equation	23
A reduced‐order modified finite difference method preserving unconditional energy‐stability for the Allen–Cahn equation	22
Numerical study and chaotic oscillations for aerodynamic model of wind turbine via fractal and fractional differential operators	22
Computational analysis of the third order dispersive fractional PDE under exponential‐decay and Mittag‐Leffler type kernels	22
Mathematical modeling of bio‐magnetic fluid bounded within ciliated walls of wavy channel	21
A high order numerical scheme for solving a class of non‐homogeneous time‐fractional reaction diffusion equation	20
A stable computational approach to analyze semi‐relativistic behavior of fractional evolutionary problems	20
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	19
Numerical and mathematical analysis of induction motor by means of AB–fractal–fractional differentiation actuated by drilling system	19
Jacobi collocation method for the fractional advection‐dispersion equation arising in porous media	19
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	18
Numerical solution of fractional partial differential equations via Haar wavelet	18
Barycentric rational method for solving biharmonic equation by depression of order	18
New results concerning to approximate controllability of fractional integro‐differential evolution equations of order 1 < r < 2	17
Simple and efficient continuous data assimilation of evolution equations via algebraic nudging	17
An inverse problem of identifying the time‐dependent potential in a fourth‐order pseudo‐parabolic equation from additional condition	17
Results on existence and controllability results for fractional evolution inclusions of order 1 < r < 2 with Clarke's subdifferential type	17
New formulas of thehigh‐orderderivatives offifth‐kindChebyshev polynomials: Spectral solution of theconvection–diffusionequation	17
Exact solutions of convective–diffusive Cahn–Hilliard equation using extended direct algebraic method	17
Approximate controllability results for Sobolev‐type delay differential system of fractional order without uniqueness	16
Decatic B‐spline collocation scheme for approximate solution of Burgers' equation	16
Novel applications of the magnetohydrodynamics couple stress fluid flows between two plates with fractal‐fractional derivatives	16
Results on approximate controllability of neutral integro‐differential stochastic system with state‐dependent delay	15
A class of new stable, explicit methods to solve the non‐stationary heat equation	15
A numerical technique based on B‐spline for a class of time‐fractional diffusion equation	15
Results on approximate controllability of Sobolev type fractional stochastic evolution hemivariational inequalities	15
Linearized stable spectral method to analyze two‐dimensional nonlinear evolutionary and reaction‐diffusion models	14
Learning parameters of a system of variable order fractional differential equations	14
Dual fractional modeling of rate type fluid throughnon‐localdifferentiation	14
Influence of thermophoretic diffusion of nanoparticles with Joule heating in flow of Maxwell nanofluid	14
A fast temporal second‐order difference scheme for the time‐fractional subdiffusion equation	13
Exact solutions of (2 + 1)‐dimensional Schrödinger's hyperbolic equation using different techniques	13
New extensions of Hermite–Hadamard inequalities via generalized proportional fractional integral	13
Unconditionally stable exponential time differencing schemes for the mass‐conserving Allen–Cahn equation with nonlocal and local effects	12
Cattaneo–Christov heat flux model for three‐dimensional magnetohydrodynamic flow of an Eyring Powell fluid over an exponentially stretching surface with convective boundary condition	11
A high‐order weighted essentially nonoscillatory scheme based on exponential polynomials for nonlinear degenerate parabolic equations	11
Combination ofShehudecomposition and variational iteration transform methods for solving fractional third order dispersive partial differential equations	11
High‐order finite difference/spectral‐Galerkin approximations for the nonlinear time–space fractional Ginzburg–Landau equation	11
Fully spectral‐Galerkin method for the one‐ and two‐dimensional fourth‐order time‐fractional partial integro‐differential equations with a weakly singular kernel	11
Heat transfer analysis on MHD flow over a stretchable Riga wall considering Entropy generation rate: A numerical study	11
An unconditionally stable algorithm for multiterm time fractional advection–diffusion equation with variable coefficients and convergence analysis	11
On solutions of fuzzy fractional order complex population dynamical model	10
Convergence analysis of the fractional decomposition method with applications to time‐fractional biological population models	10

A kernel‐based pseudo‐spectral method for multi‐term and distributed order time‐fractional diffusion equations	10
MHD two‐phase flow of Jeffrey fluid suspended with Hafnium and crystal particles: Analytical treatment	10
Numerical simulation and modeling of entropy generation in Marangoni convective flow of nanofluid with activation energy	10
The optimal homotopy analysis method applied on nonlinear time‐fractional hyperbolic partial differential equations	10
Thermal instability of magnetohydrodynamic couple stress nanofluid in rotating porous medium	9
Perturbation based analytical solutions of non‐Newtonian differential equation with heat and mass transportation between horizontal permeable channel	9
A numerical study on fractional differential equation with population growth model	9
Numerical simulation for entropy optimized nonlinear radiative flow of GO‐Al 2 O 3 magneto nanomaterials with auto catalysis chemi	9
Pattern selection in the Schnakenberg equations: From normal to anomalous diffusion	9
A non‐iterative domain decomposition method for the interaction between a fluid and a thick structure	9
A numerical analysis for fractional model of the spread of pests in tea plants	9
Numerical solution of the partial differential equations that model the steady three‐dimensional flow and heat transfer of Carreau fluid between two stretchable rotatory disks	8
Second‐order, fully decoupled, linearized, and unconditionally stable scalar auxiliary variable schemes for Cahn–Hilliard–Darcy system	8
Numerical solution of singularly perturbed 2D parabolic initial‐boundary‐value problems based on reproducing kernel theory: Error and stability analysis	8
A structure‐preserving finite element approximation of surface diffusion for curve networks and surface clusters	8
A novel approach for the solution of fractional diffusion problems with conformable derivative	8
Finite difference technique to solve a problem of generalized thermoelasticity on an annular cylinder under the effect of rotation	8
Numerical simulation of two‐dimensional and three‐dimensional generalizedKlein–Gordon–Zakharovequations with power law nonlinearity via a meshless collocation method based on barycentric ra	8
A kernel‐based method for solving the time‐fractional diffusion equation	8
A C0 linear finite element method for a second‐order elliptic equation in non‐divergence form with Cordes coefficients	8
Numerical solution of fuzzy fractional diffusion equation by Chebyshev spectral method	8
A decoupled stabilized finite element method for the dual‐porosity‐Navier–Stokes fluid flow model arising in shale oil	8
Mixed convection of ferrofluids in a square enclosure with obstacles: Effect of iso‐perimetric shapes	8
The divergence‐free nonconforming virtual element method for the Navier–Stokes problem	8
Numerical solutions of generalized Rosenau–KDV–RLW equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization	8
Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation	7
Accurate and efficient algorithms with unconditional energy stability for the time fractional Cahn–Hilliard and Allen–Cahn equations	7
On the dynamics of strong Langmuir turbulence through the five recent numerical schemes in the plasma physics	7
A fast numerical solution of the 3D nonlinear tempered fractional integrodifferential equation	7
On solutions of time‐fractional advection–diffusion equation	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
Quadratic B‐spline collocation method for time dependent singularly perturbed differential‐difference equation arising in the modeling of neuronalactivity	7
A new stable finite difference scheme and its error analysis for two‐dimensional singularly perturbed convection–diffusion equations	7
Convergence of a finite element method on a Bakhvalov‐type mesh for a singularly perturbed convection–diffusion equation in 2D	7
Numerical solution of fractional Dullin–Gottwald–Holm equation for solitary shallow water waves	7
A systematic study on weak Galerkin finite element method for second‐order parabolic problems	7
Results on approximate controllability of nondensely defined fractional neutral stochastic differential systems	7
Convective thermal conditions and the thermophoretic effect's impacts on a hybrid nanofluid over a moving thin needle	7
Numerical solutions of fractional parabolic equations with generalized Mittag–Leffler kernels	6
A higher‐order hybrid spline difference method on adaptive mesh for solving singularly perturbed parabolic reaction–diffusion problems with robin‐boundary conditions	6
Structure‐preserving exponential wave integrator methods and the long‐time convergence analysis for the Klein‐Gordon‐Dirac equation with the small coupling constant	6
Significance of bioconvection in flow of Williamson nano‐material confined by a porous radioactive Riga surface with convective Nield constrains	6
Numerical analysis of a second order ensemble method for evolutionary magnetohydrodynamics equations at small magnetic Reynolds number	6
Approximation of functions by a new type of Gamma operators	6
Displacement‐pseudostress formulation for the linear elasticity spectral problem	6
A fully‐mixed finite element method for the coupling of the Navier–Stokes and Darcy–Forchheimer equations	6
Finite element method with the total stress variable for Biot's consolidation model	6
A novel scheme for time‐fractional semi‐relativistic Vlasov–Maxwell system based on laser‐plasma interaction with linear polarization and Landau damping instability	6
A second order ensemble method with different subdomain time steps for simulating coupled surface‐groundwater flows	6
Assessment of boundary layer for flow of non‐Newtonian material induced by a moving belt with power law viscosity and thermal conductivity models	6
A second order convergent difference scheme for the initial‐boundary value problem of Korteweg–de Vires equation	6
A robust multigrid method for one dimensional immersed finite element method	6
Sharp estimates of the unique solution for two‐point fractional boundary value problems with conformable derivative	6
An effective relaxed alternating procedure for Cauchy problem connected with Helmholtz Equation	6
Weakly symmetric stress equilibration and a posteriori error estimation for linear elasticity	6
Unconditionally optimal error estimates of BDF2 Galerkin method for semilinear parabolic equation	6
A combined meshfree exponential Rosenbrock integrator for the third‐order dispersive partial differential equations	6
Efficient unconditionally stable numerical schemes for a modified phase field crystal model with a strong nonlinear vacancy potential	6
A fractional model for anomalous diffusion with increased variability: Analysis, algorithms and applications to interface problems	6
On two‐dimensional weakly singular fractional partial integro‐differential equations and dual Bernstein polynomials	5
A two‐grid finite element method for the Allen‐Cahn equation with the logarithmic potential	5
Stability and error analysis of a splitting method using Robin–Robin coupling applied to a fluid–structure interaction problem	5
Numerical solution of ABC space–time fractional distributed order reaction–diffusion equation	5
Analysis and numerical simulation of cross reaction–diffusion systems with the Caputo–Fabrizio and Riesz operators	5
A study of distributed‐order time fractional diffusion models with continuous distribution weight functions	5
Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow	5
On the numerical solution of conformable fractional diffusion problem with small delay	5
A new ϕ‐FEM approach for problems with natural boundary conditions	5
Parameter robust higher‐order finite difference method for convection‐diffusion problem with time delay	5
Local and parallel finite element methods based on two‐grid discretizations for unsteady convection–diffusion problem	5
Finite element analysis of the singularly perturbed parabolic reaction‐diffusion problems with retarded argument	5
A modified walk‐on‐sphere method for high dimensional fractional Poisson equation	5
Linearized and decoupled structure‐preserving finite difference methods and their analyses for the coupled Schrödinger–Boussinesq equations	5
Dual nature solutions for temperature‐dependent transport properties of nanofluid flow with entropy generation	5
Partial differential integral equation model for pricing American option under multi state regime switching with jumps	5
Error analysis of a fully discrete projection method for magnetohydrodynamic system	5
A numerical method based on hybrid orthonormal Bernstein and improved block‐pulse functions for solving Volterra–Fredholm integral equations	5
Numerical analysis for a class of coupled system of singularly perturbed time‐dependent convection‐diffusion equations with a discontinuous source term	5
On the sparse multiscale representation of 2‐D Burgers equations by an efficient algorithm based on multiwavelets	5

Nonconforming finite element method for coupled Poisson–Nernst–Planck equations	5
Error estimates of an operator‐splitting finite element method for the time‐dependent natural convection problem	4
On Hosoya Index and Merrifield‐Simmons Index of trees with given domination number	4
Semi‐analytic time differencing methods for singularly perturbed initial value problems	4
A new semi‐analytic solution of fractional sixth orderDrinfeld–Sokolov–Satsuma–Hirotaequation	4
The analytical solution of fractional‐order Whitham–Broer–Kaup equations by an Elzaki decomposition method	4
Conservative unconditionally stable decoupled numerical schemes for the Cahn–Hilliard–Navier–Stokes–Darcy–Boussinesq system	4
A numerical method for solving variable‐order fractional diffusion equations using fractional‐orderTaylorwavelets	4
A multipoint stress mixed finite element method for elasticity on quadrilateral grids	4
A new approach for the qualitative study of vector born disease using Caputo–Fabrizio derivative	4
Convergence analysis of single rate and multirate fixed stress split iterative coupling schemes in heterogeneous poroelastic media	4
Additive Schwarz preconditioners for C0 interior penalty methods for the obstacle problem of clamped Kirchhoff plates	4
Numerical solution ofq‐dynamic equations	4
Pulsatile Darcy flow of water‐based thermally radiative carbon nanotubes between two concentric cylinders	4
A simplified two‐level subgrid stabilized method with backtracking technique for incompressible flows at high Reynolds numbers	4
Convergence analysis of a fast second‐order time‐stepping numerical method for two‐dimensional nonlinear time–space fractional Schrödinger equation	4
Application of direct meshless local Petrov–Galerkin method for numerical solution of stochastic elliptic interface problems	4
Superlinear convergence of Anderson accelerated Newton's method for solving stationary Navier–Stokes equations	4
An interpolation method for the optimal control problem governed by the elliptic convection–diffusion equation	4
Linearized compact difference methods for solving nonlinear Sobolev equations with distributed delay	4
Finite difference schemes for the fourth‐order parabolic equations with different boundary value conditions	4
Error estimate on the tanh meshes for the time fractional diffusion equation	4
On numerical study of constrained coupled shape optimization problems based on a new shape derivative method	4
On the SAV‐DG method for a class of fourth order gradient flows	3
A simplified primal‐dual weak Galerkin finite element method for Fokker–Planck‐type equations	3
Controllability of nonlinear Hilfer fractional Langevin dynamical system	3
Convergence and superconvergence analysis for nonlinear delay reaction–diffusion system with nonconforming finite element	3
A non‐standard finite difference method for space fractional advection–diffusion equation	3
Decoupled modified characteristic finite element method for the time‐dependent Navier–Stokes/Biot problem	3
	3
Effect of magnetic field on the mixed convection in double lid‐driven porous cavities filled with micropolar nanofluids	3
Decoupled and linearized scalar auxiliary variable finite element method for the time‐dependent incompressible magnetohydrodynamic equations: Unconditional stability and convergence analysis	3
Numerical simulations for the predator–prey model as a prototype of an excitable system	3
The analysis of the solution of the Burgers–Huxley equation using the Galerkin method	3
A study over with four‐parameter Logistic and Gompertz growth models	3
Convergence and error estimation of weighted finite volume scheme for coagulation‐fragmentation equation	3
Analysis of the parareal approach based on discontinuous Galerkin method for time‐dependent Stokes equations	3
Error estimation for second‐order partial differential equations in nonvariational form	3
Fourth‐order compact scheme based on quasi‐variable mesh for three‐dimensional mildly nonlinear stationary convection–diffusion equations	3
A comparative study on non‐Newtonian fractional‐order Brinkman type fluid with two different kernels	3
Half inverse problem for diffusion operators with jump conditions dependent on the spectral parameter	3
Virtual element method for elliptic bulk‐surface PDEs in three space dimensions	3
Optimal error estimates of fourth‐order compact finite difference methods for the nonlinear Klein–Gordon equation in the nonrelativistic regime	3
Solving the2Dand3Dnonlinear inverse source problems of elliptic type partial differential equations by a homogenization function method	3
An oscillation free local discontinuous Galerkin method for nonlinear degenerate parabolic equations	3
	3
Efficient quadrature rules for finite element discretizations of nonlocal equations	3
A fourth‐order accurate numerical method for the distributed‐order Riesz space fractional diffusion equation	3
Improved a priori error estimates for a discontinuous Galerkin pressure correction scheme for the Navier–Stokes equations	3
A superlinear convergence scheme for the multi‐term and distribution‐order fractional wave equation with initial singularity	3
On the application of a Krylov subspace spectral method to poroacoustic shocks in inhomogeneous gases	3
A pressure‐robust weak Galerkin finite element method for Navier–Stokes equations	3
Block preconditioners for energy stable schemes of magnetohydrodynamics equations	3
A fractional system of Cauchy‐reaction diffusion equations by adopting Robotnov function	3
Mathematical model for the novel coronavirus (2019‐nCOV) with clinical data using fractional operator	3
A posteriori error estimates for the large eddy simulation applied to stationary Navier–Stokes equations	3
An artificial neural network‐based method for the optimal control problem governed by the fractional parabolic equation	3
Analytical and numerical techniques for initial‐boundary value problems of Kolmogorov–Petrovsky–Piskunov equation	3
An unconditionally stable artificial compression method for the time‐dependent groundwater‐surface water flows	3
	2
Using radial basis function‐generated quadrature rules to solve nonlocal continuum models	2
Numerical analysis of a corrected Smagorinsky model	2
Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise	2
A novel local Hermite radial basis function‐based differential quadrature method for solving two‐dimensional variable‐order time fractional advection–diffusion equation with Neumann boundary condition	2
A new stable, explicit, and generic third‐order method for simulating conductive heat transfer	2
Porous exponential domination number of some graphs	2
Development of data‐driven exponential integrators with application to modeling of delay photocurrents	2
A fuzzy solution of wave equation by FFS‐transform	2
High order accurate method for the numerical solution of the second order linear hyperbolic telegraph equation	2
An improved numerical technique for distributed‐order time‐fractional diffusion equations	2
A mixed element analysis of the Biot's model with Darcy–Forchheimer flow	2
On rigorous computational and numerical solutions for the voltages of the electrified transmission range with the day yet distance	2
Numerical approximation of the optimal control of a population dynamics model	2
A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation	2
Global and local structure‐based influential nodes identification in wheel‐type networks	2
Some new integral inequalities associated with generalized proportional fractional operators	2
Time–space Jacobi pseudospectral simulation of multidimensional Schrödinger equation	2
On the phase separation in the ternary alloys: Numerical and computational simulations of the Atangana–Baleanu time‐fractional Cahn–Allen equation	2
A Cα finite difference method for the Caputo time‐fractional diffusion equation	2
Adaptive stochastic gradient descent for optimal control of parabolic equations with random parameters	2
TheBDF2 FDMfor the fourth‐order equations with the multi‐termR‐Lfractional integral kernels	2
A C0 interior penalty method for the phase field crystal equation	2
Double diffusive effects on nanofluid flow toward a permeable stretching surface in presence of Thermophoresis and Brownian motion effects: A numerical study	2
Integrated radial basis functions to simulate modified anomalous sub‐diffusion equation	2
A mixed finite element method for the Poisson problem using a biorthogonal system with Raviart–Thomas elements	2
	2
Some special functions in orthogonal fuzzy bipolar metric spaces and their fixed point applications	2
Multiphysics mixed finite element method with Nitsche's technique for Stokes‐poroelasticity problem	2
Experimental convergence rate study for three shock‐capturing schemes and development of highly accurate combined schemes	2
Lp error estimate of nonlinear Schrödinger equation using a two‐grid finite element method	2
Simulation of the interaction of light with 3‐D metallic nanostructures using a proper orthogonal decomposition‐Galerkin reduced‐order discontinuous Galerkin time‐domain method	2
A conservative difference scheme with optimal pointwise error estimates for two‐dimensional space fractional nonlinear Schrödinger equations	2
A quartic trigonometric tension B‐spline finite element method for solving Gardner equation	2
On the convergence and superconvergence for a class of two‐dimensional time fractional reaction‐subdiffusion equations	2
Operator splitting for the fractional Korteweg‐de Vries equation	2