An efficient parallel approximate algorithm for solving time fractional reaction-diffusion equations
type: Item
instance of: scholarly article
title: An efficient parallel approximate algorithm for solving time fractional reaction-diffusion equations
zbMATH Open document ID: 1459.65163
DOI: 10.1155/2020/4524387
author: Lifei Wu
author: Xiaozhong Yang
published in: Mathematical Problems in Engineering
publication date: 2020-10-12T00:00:00Z
review text: Summary: In this paper, we construct pure alternative segment explicit-implicit (PASE-I) and implicit-explicit (PASI-E) difference algorithms for time fractional reaction-diffusion equations (FRDEs). They are a kind of difference schemes with intrinsic parallelism and based on classical explicit scheme and classical implicit scheme combined with alternating segment technology. The existence and uniqueness analysis of solutions of the parallel difference schemes are given. Both the theoretical proof and the numerical experiment show that PASE-I and PASI-E schemes are unconditionally stable and convergent with second-order spatial accuracy and \(2-\alpha\) order time accuracy. Compared with implicit scheme and E-I (I-E) scheme, the computational efficiency of PASE-I and PASI-E schemes is greatly improved. PASE-I and PASI-E schemes have obvious parallel computing properties, which shows that the difference schemes with intrinsic parallelism in this paper are feasible to solve the time FRDEs.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 7259608
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/4524387
OpenAlex ID: W3080709529
cites work: Fractional derivatives for physicists and engineers. Volume I: Background and theory. Volume II: Applications
cites work: On a fractional reaction-diffusion system applied to image decomposition and restoration
cites work: Q4233638
cites work: A new collection of real world applications of fractional calculus in science and engineering
cites work: Fractional Partial Differential Equations and Their Numerical Solutions
cites work: High Accuracy Algorithm for the Differential Equations Governing Anomalous Diffusion
cites work: Fractional differentiation matrices with applications
cites work: A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications
cites work: Numerical computation and stability analysis for the fractional subdiffusions with spatial variable coefficients
cites work: A second-order accurate numerical approximation for the fractional diffusion equation
cites work: A compact finite difference scheme for the fractional sub-diffusion equations
cites work: Quadratic spline collocation method for the time fractional subdiffusion equation
cites work: A finite difference scheme based on cubic trigonometric B-splines for a time fractional diffusion-wave equation
cites work: A Second-Order Accurate Implicit Difference Scheme for Time Fractional Reaction-Diffusion Equation with Variable Coefficients and Time Drift Term
cites work: An efficient and uniformly convergent scheme for one-dimensional parabolic singularly perturbed semilinear systems of reaction-diffusion type
cites work: The local discontinuous Galerkin finite element methods for Caputo-type partial differential equations: numerical analysis
cites work: The local discontinuous Galerkin finite element methods for Caputo-type partial differential equations: mathematical analysis
cites work: Q5436184
cites work: A direct \(O(N \log ^{2} N)\) finite difference method for fractional diffusion equations
cites work: Fast approximate inversion of a block triangular Toeplitz matrix with applications to fractional sub‐diffusion equations
cites work: Fast iterative method with a second-order implicit difference scheme for time-space fractional convection-diffusion equation
cites work: Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations
cites work: A limited-memory block bi-diagonal Toeplitz preconditioner for block lower triangular Toeplitz system from time-space fractional diffusion equation
cites work: Group explicit methods for parabolic equations
cites work: Alternating segment explicit-implicit scheme for nonlinear third-order KdV equation
cites work: Unconditional stability of parallel difference schemes with second order accuracy for parabolic equation
cites work: An efficient parallel algorithm for the numerical solution of fractional differential equations
cites work: A parallel algorithm for the Riesz fractional reaction-diffusion equation with explicit finite difference method
cites work: A parallel Crank-Nicolson finite difference method for time-fractional parabolic equation
cites work: An efficient parallel algorithm for Caputo fractional reaction-diffusion equation with implicit finite-difference method
cites work: Parallel algorithms for nonlinear time-space fractional parabolic PDEs
cites work: A preconditioned fast parareal finite difference method for space-time fractional partial differential equation
cites work: A class of efficient difference method for time fractional reaction-diffusion equation
cites work: Partial differential equations: Modeling, analysis and numerical approximation
cites work: Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
description: scientific article; zbMATH DE number 7259608