A novel finite difference technique with error estimate for time fractional partial integro-differential equation of Volterra type

DOI10.1016/j.cam.2021.113746zbMath1496.65128OpenAlexW3184571463WikidataQ114201976 ScholiaQ114201976MaRDI QIDQ2229935

Yanyan Li

Publication date: 17 September 2021

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2021.113746

zbMATH Keywords

error analysisCaputo fractional derivativepartial integro-differential equationL1 scheme

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Finite difference methods for boundary value problems involving PDEs (65N06) Volterra integral equations (45D05) Fractional partial differential equations (35R11) Integro-partial differential equations (35R09)

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Cites Work

• Existence and attractivity results for some fractional order partial integro-differential equations with delay
• A new operational matrix based on Bernoulli wavelets for solving fractional delay differential equations
• Finite central difference/finite element approximations for parabolic integro-differential equations
• On existence and uniqueness of solutions of a nonlinear integral equation
• Uniform difference method for singularly perturbed Volterra integro-differential equations
• Numerical methods for fourth-order fractional integro-differential equations
• Solving multi-term linear and non-linear diffusion-wave equations of fractional order by Adomian decomposition method
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• A review of the decomposition method in applied mathematics
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• The existence and uniqueness of the solution for nonlinear Fredholm and Volterra integral equations together with nonlinear fractional differential equations via \( w\)-distances
• Convergence in positive time for a finite difference method applied to a fractional convection-diffusion problem
• Existence and uniqueness of solutions for a class of nonlinear integro-differential equations on unbounded domains in Banach spaces
• A numerical method for solving linear integral equations of the second kind on the non-rectangular domains based on the meshless method
• A high order finite volume element method for solving elliptic partial integro-differential equations
• Numerical solution of partial integrodifferential equations of diffusion type
• A Tau-like numerical method for solving fractional delay integro-differential equations
• The Puiseux expansion and numerical integration to nonlinear weakly singular Volterra integral equations of the second kind
• The bivariate Müntz wavelets composite collocation method for solving space-time-fractional partial differential equations
• Weak Galerkin finite element method for the parabolic integro-differential equation with weakly singular kernel
• A new numerical method for solving fractional delay differential equations
• Approximate solution of nonlinear fractional integro-differential equations using fractional alternative Legendre functions
• Space-time spectral method for a weakly singular parabolic partial integro-differential equation on irregular domains
• Numerical solution of fractional integro-differential equations by collocation method
• Numerical solution of the general form linear Fredholm-Volterra integro-differential equations by the tau method with an error estimation
• Solution of a partial integro-differential equation arising from viscoelasticity
• Integral equations arising in the kinetic theory of gases
• A COMPUTATIONAL METHOD FOR SOLVING TWO-DIMENSIONAL LINEAR FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND
• A Numerical Method for a Partial Integro-Differential Equation
• Modified Laplace decomposition method for fractional Volterra-Fredholm integro-differential equations
• A numerical scheme based on Bernoulli wavelets and collocation method for solving fractional partial differential equations with Dirichlet boundary conditions
• Analysis of the L1 scheme for a time fractional parabolic–elliptic problem involving weak singularity
• A uniformly convergent numerical method for a singularly perturbed Volterra integro-differential equation
• A perturbation-based approach for solving fractional-order Volterra–Fredholm integro differential equations and its convergence analysis
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• Richardson extrapolation of iterated discrete Galerkin solution for two-dimensional Fredholm integral equations
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• Unnamed Item