Alternating direction implicit Euler method for the high-dimensional evolution equations with weakly singular kernel

DOI10.12286/jssx.j2021-0818MaRDI QIDQ6665182

Xuehua Yang, Haixiang Zhang, Yan-Ling Liu

Publication date: 17 January 2025

Published in: Mathematica Numerica Sinica (Search for Journal in Brave)

zbMATH Keywords

evolution equationsfinite difference methodsbackward Euler methodalternating direction implicit methoddiscrete energy method

Mathematics Subject Classification ID

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)

Cites Work

• Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation
• A finite difference scheme for partial integro-differential equations with a weakly singular kernel
• An implicit difference scheme and algorithm implementation for the one-dimensional time-fractional Burgers equations
• Alternating direction implicit-Euler method for the two-dimensional fractional evolution equation
• A compact difference scheme for an evolution equation with a weakly singular kernel
• Compact Alternating Direction Implicit Scheme for the Two-Dimensional Fractional Diffusion-Wave Equation
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• Ritz–Volterra Projections to Finite-Element Spaces and Applications to Integrodifferential and Related Equations
• A Difference Scheme for a Nonlinear Partial Integrodifferential Equation
• A second-order accurate numerical method for a semilinear integro-differential equation with a weakly singular kernel
• Time Discretization of an Integro-Differential Equation of Parabolic Type
• Finite element methods for parabolic and hyperbolic partial integro-differential equations
• An Abstract Parabolic Volterra Integrodifferential Equation
• Numerical solution of an evolution equation with a positive-type memory term
• Solving Degenerate Reaction-Diffusion Equations via Variable Step Peaceman--Rachford Splitting
• A formally second order BDF ADI difference scheme for the three-dimensional time-fractional heat equation
• A backward Euler difference scheme for the integro-differential equations with the multi-term kernels
• A high-order compact ADI method for solving three-dimensional unsteady convection-diffusion problems
• Volterra Integral Equations in Banach Space

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