Implicit Runge-Kutta and spectral Galerkin methods for the two-dimensional nonlinear Riesz space distributed-order diffusion equation

DOI10.1016/j.apnum.2020.06.003zbMath1446.65136OpenAlexW3036119632MaRDI QIDQ2192620

Jingjun Zhao, Yanming Zhang, Yang Xu

Publication date: 17 August 2020

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2020.06.003

zbMATH Keywords

stabilityconvergenceimplicit Runge-Kutta methodspectral Galerkin methodGauss quadrature formulanonlinear Riesz space distributed-order diffusion equation

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Fractional derivatives and integrals (26A33) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical quadrature and cubature formulas (65D32) Fractional partial differential equations (35R11)

Related Items (4)

General linear and spectral Galerkin methods for the nonlinear two-sided space distributed-order diffusion equation ⋮ Solutions for a singular Hadamard-type fractional differential equation by the spectral construct analysis ⋮ Error estimates of local discontinuous Galerkin method with implicit-explicit Runge Kutta for two-phase miscible flow in porous media ⋮ Finite difference/spectral element method for one and two-dimensional Riesz space fractional advection-dispersion equations

Uses Software

• RODAS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Error estimates for approximations of distributed order time fractional diffusion with nonsmooth data
• Novel second-order accurate implicit numerical methods for the Riesz space distributed-order advection-dispersion equations
• Numerical solution for diffusion equations with distributed order in time using a Chebyshev collocation method
• Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
• Numerical analysis for distributed-order differential equations
• A block-centered finite difference method for the distributed-order time-fractional diffusion-wave equation
• A numerical method for solving the two-dimensional distributed order space-fractional diffusion equation on an irregular convex domain
• New compact difference scheme for solving the fourth-order time fractional sub-diffusion equation of the distributed order
• Local discontinuous Galerkin method for distributed-order time and space-fractional convection-diffusion and Schrödinger-type equations
• Finite difference/spectral-Galerkin method for a two-dimensional distributed-order time-space fractional reaction-diffusion equation
• An efficient split-step method for distributed-order space-fractional reaction-diffusion equations with time-dependent boundary conditions
• Efficient high-order compact exponential time differencing method for space-fractional reaction-diffusion systems with nonhomogeneous boundary conditions
• A Crank-Nicolson ADI Galerkin-Legendre spectral method for the two-dimensional Riesz space distributed-order advection-diffusion equation
• A novel finite volume method for the Riesz space distributed-order advection-diffusion equation
• An efficient finite volume method for nonlinear distributed-order space-fractional diffusion equations in three space dimensions
• Some high-order difference schemes for the distributed-order differential equations
• Finite difference/spectral approximations for the distributed order time fractional reaction-diffusion equation on an unbounded domain
• Finite difference/finite element methods for distributed-order time fractional diffusion equations
• Variational solution of fractional advection dispersion equations on bounded domains in ℝd
• Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equations with a weakly singular kernel
• UNIFORM INF–SUP CONDITIONS FOR THE SPECTRAL DISCRETIZATION OF THE STOKES PROBLEM
• Analysis of Spectral Projectors in One-Dimensional Domains
• Runge-Kutta Approximation of Quasi-Linear Parabolic Equations
• Second-order predictor-corrector schemes for nonlinear distributed-order space-fractional differential equations with non-smooth initial data
• Numerical analysis for the time distributed-order and Riesz space fractional diffusions on bounded domains

This page was built for publication: Implicit Runge-Kutta and spectral Galerkin methods for the two-dimensional nonlinear Riesz space distributed-order diffusion equation