Numerical Methods for Partial Differential Equations

Article	Citations
A wavelet based numerical scheme for fractional order SEIR epidemic of measles by using Genocchi polynomials	146
A study on fractional host–parasitoid population dynamical model to describe insect species	89
The reducing rank method to solve third‐order Duffing equation with the homotopy perturbation	74
Numerical investigations on COVID‐19 model through singular and non‐singular fractional operators	74
New numerical simulation for fractional Benney–Lin equation arising in falling film problems using two novel techniques	73
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	73
He's frequency formulation for fractal nonlinear oscillator arising in a microgravity space	65
Microorganisms swimming through radiative Sutterby nanofluid over stretchable cylinder: Hydrodynamic effect	58
Analytical and numerical approaches to nerve impulse model of fractional‐order	57
A generalized differential quadrature algorithm for simulating magnetohydrodynamic peristaltic flow of blood‐based nanofluid containing magnetite nanoparticles: A physiological application	56
A mathematical analysis of ongoing outbreakCOVID‐19 in India through nonsingular derivative	55
Results on approximate controllability results for second‐order Sobolev‐type impulsive neutral differential evolution inclusions with infinite delay	54
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	49
A new study on existence and uniqueness of nonlocal fractional delay differential systems of order 1 < r < 2 in Banach spaces	48
European option pricing models described by fractional operators with classical and generalizedMittag‐Lefflerkernels	47
Boundary layer flow pattern of heat and mass for homogenous shear thinning hybrid‐nanofluid: An experimental data base modeling	45
A new exploration on existence of Sobolev‐type Hilfer fractional neutral integro‐differential equations with infinite delay	45
A fractional model for population dynamics of two interacting species by using spectral and Hermite wavelets methods	43
Mathematical modeling for novel coronavirus (COVID‐19) and control	42
An efficient numerical approach for fractional multidimensional diffusion equations with exponential memory	42
Mathematical model for spreading of COVID‐19 virus with the Mittag–Leffler kernel	41
Implicit meshless method to solve 2D fractional stochastic Tricomi‐type equation defined on irregular domain occurring in fractal transonic flow	38
Numerical solutions for solving model time‐fractionalFokker–Planckequation	38
Existence and controllability of nonlocal mixed Volterra‐Fredholm type fractional delay integro‐differential equations of order 1 < r < 2	35

Generalized differential quadrature scrutinization of an advanced MHD stability problem concerned water‐based nanofluids with metal/metal oxide nanomaterials: A prop	35
New discussion on approximate controllability results for fractional Sobolev type Volterra‐Fredholm integro‐differential systems of order 1 < r < 2	35
A novel numerical manner for two‐dimensional space fractional diffusion equation arising in transport phenomena	34
Heat and mass transfer analysis for bioconvective flow of Eyring Powell nanofluid over a Riga surface with nonlinear thermal features	34
Linear barycentric rational collocation method for solving heat conduction equation	34
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	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
Legendre wavelet collocation method for fractional optimal control problems with fractional Bolza cost	30
A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions	29
Numerical solutions of distributed order fractional differential equations in the time domain using the Müntz–Legendre wavelets approach	29
Computational investigation of heat transfer in a flow subjected to magnetohydrodynamic of Maxwell nanofluid over a stretched flat sheet with thermal radiation	28
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
Integrated neuro‐evolution heuristic with sequential quadratic programming for second‐order prediction differential models	26
A study over the general formula of regression sum of squares in multiple linear regression	25
Numerical approach to chaotic pattern formation in diffusive predator–prey system with Caputo fractional operator	25
An efficient computational technique for time‐fractionalKaup‐Kupershmidtequation	24
Finite difference/collocation method to solve multi term variable‐order fractional reaction–advection–diffusion equation in heterogeneous medium	24
An efficient tool for solving two‐dimensional fuzzy fractional‐ordered heat equation	24
On the nondifferentiable exact solutions to Schamel's equation with local fractional derivative on Cantor sets	24
Controlled fuzzy metric spaces and some related fixed point results	24
Computational analysis of the third order dispersive fractional PDE under exponential‐decay and Mittag‐Leffler type kernels	23
Modeling and numerical investigation of fractional‐order bovine babesiosis disease	23
Computational examination of Casson nanofluid due to a non‐linear stretching sheet subjected to particle shape factor: Tiwari and Das model	23
Numerical and theoretical discussions for solving nonlinear generalized Benjamin–Bona–Mahony–Burgers equation based on the Legendre spectral element method	23
A local hybrid kernel meshless method for numerical solutions of two‐dimensional fractional cable equation in neuronal dynamics	22
A robust scheme based on novel‐operational matrices for some classes of time‐fractional nonlinear problems arising in mechanics and mathematical physics	22
Comparison between the new exact and numerical solutions of the Mikhailov–Novikov–Wang equation	21
Long time error analysis of the fourth‐order compact finite difference methods for the nonlinear Klein–Gordon equation with weak nonlinearity	21
A reduced‐order modified finite difference method preserving unconditional energy‐stability for the Allen–Cahn equation	21
Weighted Hermite–Hadamard–Mercer type inequalities for convex functions	21
A stable computational approach to analyze semi‐relativistic behavior of fractional evolutionary problems	20
Investigation of Coriolis effect on oceanic flows and its bifurcation via geophysical Korteweg–de Vries equation	20
Analysis of a momentum conservative mixed‐FEM for the stationary Navier–Stokes problem	20
Barycentric rational interpolation and local radial basis functions based numerical algorithms for multidimensional sine‐Gordon equation	20
A fast implicit difference scheme for solving the generalized time–space fractional diffusion equations with variable coefficients	20
A high order numerical scheme for solving a class of non‐homogeneous time‐fractional reaction diffusion equation	20
Numerical and mathematical analysis of induction motor by means of AB–fractal–fractional differentiation actuated by drilling system	20
A study on fractional predator–prey–pathogen model with Mittag–Leffler kernel‐based operators	19
Mathematical modeling of bio‐magnetic fluid bounded within ciliated walls of wavy channel	19
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	18
Jacobi collocation method for the fractional advection‐dispersion equation arising in porous media	18
A two‐grid method with backtracking for the mixed Navier–Stokes/Darcy model	18
Barycentric rational method for solving biharmonic equation by depression of order	18
A Haar wavelet collocation approach for solving one and two‐dimensional second‐order linear and nonlinear hyperbolic telegraph equations	18
A stabilizer free weak Galerkin finite element method with supercloseness of order two	18
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
The fast scalar auxiliary variable approach with unconditional energy stability for nonlocal Cahn–Hilliard equation	17
A reduced‐order extrapolating space–time continuous finite element method for the 2D Sobolev equation	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
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	16
The pointwise estimates of a conservative difference scheme for Burgers' equation	16
Dual fractional modeling of rate type fluid through non‐local differentiation	16
Effects of radiative heat flux and heat generation on magnetohydodynamics natural convection flow of nanofluid inside a porous triangular cavity with thermal boundary conditions	16
Results on existence and controllability results for fractional evolution inclusions of order 1 < r < 2 with Clarke's subdifferential type	16
On solution of a class of nonlinear variable order fractional reaction–diffusion equation with Mittag–Leffler kernel	15
A parameter‐uniform scheme for the parabolic singularly perturbed problem with a delay in time	15
An inverse problem of identifying the time‐dependent potential in a fourth‐order pseudo‐parabolic equation from additional condition	15
Structure of analytical and symbolic computational approach of multiple solitary wave solutions for nonlinear Zakharov‐Kuznetsov modified equal width equation	15
Results on approximate controllability of neutral integro‐differential stochastic system with state‐dependent delay	15
An improvised collocation algorithm with specific end conditions for solving modified Burgers equation	15
Results on approximate controllability of Sobolev type fractional stochastic evolution hemivariational inequalities	15
Numerical solution of fractional partial differential equations via Haar wavelet	15
Simple and efficient continuous data assimilation of evolution equations via algebraic nudging	14
Approximate controllability results for Sobolev‐type delay differential system of fractional order without uniqueness	14
Linearized stable spectral method to analyze two‐dimensional nonlinear evolutionary and reaction‐diffusion models	14
Decatic B‐spline collocation scheme for approximate solution of Burgers' equation	13
Analytical and numerical solutions of the Fitzhugh–Nagumo equation and their multistability behavior	13
Finite difference method combined with differential quadrature method for numerical computation of the modified equal width wave equation	13
Novel applications of the magnetohydrodynamics couple stress fluid flows between two plates with fractal‐fractional derivatives	13
Influence of thermophoretic diffusion of nanoparticles with Joule heating in flow of Maxwell nanofluid	13
A new high‐order weighted essentially non‐oscillatory scheme for non‐linear degenerate parabolic equations	13
On the absolute stable difference scheme for the space‐wise dependent source identification problem for elliptic‐telegraph equation	12
The numerical analysis of two linearized difference schemes for the Benjamin–Bona–Mahony–Burgers equation	12
Soret–Dufour mechanism on an electrically conducting nanofluid flow past a semi‐infinite porous plate with buoyancy force and chemical reaction influence	12
On refinements of some integral inequalities using improved power‐mean integral inequalities	12
On Romanovski–Jacobi polynomials and their related approximation results	11
New extensions of Hermite–Hadamard inequalities via generalized proportional fractional integral	11
High‐order finite difference/spectral‐Galerkin approximations for the nonlinear time–space fractional Ginzburg–Landau equation	11
Optimal uniform error estimates for moving least‐squares collocation with application to option pricing under jump‐diffusion processes	11
A numerical technique based on B‐spline for a class of time‐fractional diffusion equation	11
Heat transfer analysis on MHD flow over a stretchable Riga wall considering Entropy generation rate: A numerical study	11
Weak Galerkin finite element method for a class of time fractional generalized Burgers' equation	11
A fast temporal second‐order difference scheme for the time‐fractional subdiffusion equation	11
Half‐inverse problems for the quadratic pencil of the Sturm–Liouville equations with impulse	11
Analysis of a novel finance chaotic model via ABC fractional derivative	11
Learning parameters of a system of variable order fractional differential equations	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
Approximation of functions by a new construction of Bernstein‐Chlodowsky operators: Theory and applications	10
Unconditionally stable exponential time differencing schemes for the mass‐conserving Allen–Cahn equation with nonlocal and local effects	10
Cattaneo–Christov heat flux model for three‐dimensional magnetohydrodynamic flow of an Eyring Powell fluid over an exponentially stretching surface with convective boundary condition	10
Exact solutions of (2 + 1)‐dimensional Schrödinger's hyperbolic equation using different techniques	9
CVFEM based numerical investigation and mathematical modeling of surface dependent magnetized copper‐oxide nanofluid flow using new model of porous space	9
A numerical analysis for fractional model of the spread of pests in tea plants	9
The optimal homotopy analysis method applied on nonlinear time‐fractional hyperbolic partial differential equations	9
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
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
Numerical wavelets scheme to complex partial differential equation arising from Morlet continuous wavelet transform	9
A high‐order weighted essentially nonoscillatory scheme based on exponential polynomials for nonlinear degenerate parabolic equations	9
The divergence‐free nonconforming virtual element method for the Navier–Stokes problem	9
Simultaneous inversion of two initial values for a time‐fractional diffusion‐wave equation	9
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
Fully spectral‐Galerkin method for the one‐ and two‐dimensional fourth‐order time‐fractional partial integro‐differential equations with a weakly singular kernel	8
Combination of Shehu decomposition and variational iteration transform methods for solving fractional third order dispersive partial differential equations	8
Compact difference scheme for two‐dimensional fourth‐order nonlinear hyperbolic equation	8
Numerical solution of fuzzy fractional diffusion equation by Chebyshev spectral method	8
Numerical solution of the multiterm time‐fractional diffusion equation based on reproducing kernel theory	8
MHD two‐phase flow of Jeffrey fluid suspended with Hafnium and crystal particles: Analytical treatment	8
On solutions of fuzzy fractional order complex population dynamical model	8
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	7
Existence and uniqueness of solutions for fractional nonlinear hybrid impulsive system	7
Fast calculation based on a spatial two‐grid finite element algorithm for a nonlinear space–time fractional diffusion model	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
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 C0 linear finite element method for a second‐order elliptic equation in non‐divergence form with Cordes coefficients	7
A modified Chebyshev ϑ‐weighted Crank–Nicolson method for analyzing fractional sub‐diffusion equations	7
Second‐order, fully decoupled, linearized, and unconditionally stable scalar auxiliary variable schemes for Cahn–Hilliard–Darcy system	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
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
Thermal instability of magnetohydrodynamic couple stress nanofluid in rotating porous medium	7

Dynamics of Arrhenius activation energy in flow of Carreau fluid subject to Brownian motion diffusion	7
Reproducing kernel method to solve parabolic partial differential equations with nonlocal conditions	7
Analysis and efficient implementation of alternating direction implicit finite volume method for Riesz space‐fractional diffusion equations in two space dimensions	7
Perturbation based analytical solutions of non‐Newtonian differential equation with heat and mass transportation between horizontal permeable channel	7
Results on approximate controllability of nondensely defined fractional neutral stochastic differential systems	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