Explicit Exponential Runge–Kutta Methods for Semilinear Integro-Differential Equations

DOI10.1137/22m1504056zbMath1516.65154arXiv2206.05849OpenAlexW4380089432MaRDI QIDQ6156606

Fardin Saedpanah, Alexander Ostermann, Unnamed Author

Publication date: 14 June 2023

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.05849

zbMATH Keywords

convergenceRunge-Kutta methodsorder conditionsexponential integratorssemilinear integro-differential equation

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Cites Work

• A family of Adams exponential integrators for fractional linear systems
• Generalized integrating factor methods for stiff PDEs
• Semigroups of linear operators and applications to partial differential equations
• Geometric theory of semilinear parabolic equations
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Exponential Runge-Kutta methods for parabolic problems.
• Existence, uniqueness and regularity for a class of semilinear stochastic Volterra equations with multiplicative noise
• Exponential integrators
• FRACTIONAL DIFFUSIVE WAVES
• Convolution quadrature time discretization of fractional diffusion-wave equations
• A Numerical Method for a Partial Integro-Differential Equation
• Finite Element Approximation of a Parabolic Integro-Differential Equation with a Weakly Singular Kernel
• Evolutionary Integral Equations and Applications
• Numerical solution of an evolution equation with a positive-type memory term
• A Numerical Method for an Integro-Differential Equation with Memory in Banach Spaces: Qualitative Properties
• Runge-Kutta Approximation of Quasi-Linear Parabolic Equations
• Linearly implicit time discretization of non-linear parabolic equations
• Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term
• Mittag--Leffler Euler Integrator for a Stochastic Fractional Order Equation with Additive Noise
• Fourth-Order Time-Stepping for Stiff PDEs
• Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems