Higher order approximations for fractional order integro-parabolic partial differential equations on an adaptive mesh with error analysis

DOI10.1016/j.camwa.2023.09.008OpenAlexW4387116709MaRDI QIDQ6062193

Sudarshan Santra, Debajyoti Choudhuri, Jugal Mohapatra, Pratibhamoy Das

Publication date: 30 November 2023

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2023.09.008

zbMATH Keywords

convergence analysisexistence and uniquenessweakly singular kernelVolterra integralfractional order parabolic equationshigher-order estimate on graded mesh

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Fractional derivatives and integrals (26A33) 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) Fractional partial differential equations (35R11) Numerical analysis (65-XX)

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Cites Work

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• Collocation methods for fractional integro-differential equations with weakly singular kernels
• Solving metamaterial Maxwell's equations via a vector wave integro-differential equation
• A new computational method based on fractional Lagrange functions to solve multi-term fractional differential equations
• High-order compact ADI methods for parabolic equations
• Müntz-Legendre wavelet operational matrix of fractional-order integration and its applications for solving the fractional pantograph differential equations
• Global pointwise error estimates for uniformly convergent finite element methods for the elliptic boundary layer problem
• Numerical methods for a class of nonlinear integro-differential equations
• Convergence of numerical schemes for the solution of partial integro-differential equations used in heat transfer
• Higher order accurate approximations on equidistributed meshes for boundary layer originated mixed type reaction diffusion systems with multiple scale nature
• A priori error analysis for a finite element approximation of dynamic viscoelasticity problems involving a fractional order integro-differential constitutive law
• An implicit semi-linear discretization of a bi-fractional Klein-Gordon-Zakharov system which conserves the total energy
• On a discrete model that dissipates the free energy of a time-space fractional generalized nonlinear parabolic equation
• On the approximate solutions of a class of fractional order nonlinear Volterra integro-differential initial value problems and boundary value problems of first kind and their convergence analysis
• Arbitrary high-order methods for one-sided direct event location in discontinuous differential problems with nonlinear event function
• Error analysis of a finite difference method on graded meshes for a multiterm time-fractional initial-boundary value problem
• Numerical solutions of time-fractional partial integrodifferential equations of Robin functions types in Hilbert space with error bounds and error estimates
• Existence of solutions of an explicit energy-conserving scheme for a fractional Klein-Gordon-Zakharov system
• Finite element method for two-sided fractional differential equations with variable coefficients: Galerkin approach
• A singular system involving the fractional \(p\)-Laplacian operator via the Nehari manifold approach
• An a posteriori based convergence analysis for a nonlinear singularly perturbed system of delay differential equations on an adaptive mesh
• A link between a variable-order fractional Zener model and non-Newtonian time-varying viscosity for viscoelastic material: relaxation time
• Computational cost reduction for coupled system of multiple scale reaction diffusion problems with mixed type boundary conditions having boundary layers
• ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS OF FRACTIONAL ORDER PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• Theoretical prospects of fractional order weakly singular Volterra Integro differential equations and their approximations with convergence analysis
• A perturbation-based approach for solving fractional-order Volterra–Fredholm integro differential equations and its convergence analysis
• A graded mesh refinement approach for boundary layer originated singularly perturbed time‐delayed parabolic convection diffusion problems
• Analysis of a finite difference method based on L1 discretization for solving multi‐term fractional differential equation involving weak singularity
• A higher order hybrid-numerical approximation for a class of singularly perturbed two-dimensional convection-diffusion elliptic problem with non-smooth convection and source terms
• Transient vibrations of a fractional Zener viscoelastic cantilever beam with a tip mass