Efficient and Stable Exponential Runge-Kutta Methods for Parabolic Equations

DOI10.4208/aamm.2015.m1045zbMath1488.65325OpenAlexW2530988098WikidataQ115481497 ScholiaQ115481497MaRDI QIDQ5155223

Liyong Zhu

Publication date: 6 October 2021

Published in: Advances in Applied Mathematics and Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/aamm.2015.m1045

zbMATH Keywords

explicit schemeAllen-Cahn equationexponential Runge-Kutta methodlinear splittingdiscrete fast Fourier transforms

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical methods for discrete and fast Fourier transforms (65T50) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Complexity and performance of numerical algorithms (65Y20) Numerical methods for stiff equations (65L04) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items (2)

An adaptive time-stepping algorithm for the Allen-Cahn equation ⋮ An unconditionally energy stable second order finite element method for solving the Allen-Cahn equation

Cites Work

• Unnamed Item
• Array-representation integration factor method for high-dimensional systems
• An unconditionally stable hybrid numerical method for solving the Allen-Cahn equation
• Exponential time differencing for stiff systems
• Generalized integrating factor methods for stiff PDEs
• Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method
• Compact integration factor methods in high spatial dimensions
• Explicit exponential Runge-Kutta methods of high order for parabolic problems
• Fast explicit integration factor methods for semilinear parabolic equations
• Analysis and applications of the exponential time differencing schemes and their contour integration modifications
• Exponential integrators
• Numerical Studies of Discrete Approximations to the Allen–Cahn Equation in the Sharp Interface Limit
• Exponential Integrators for Large Systems of Differential Equations
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• Stability properties of explicit exponential Runge-Kutta methods
• Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems

This page was built for publication: Efficient and Stable Exponential Runge-Kutta Methods for Parabolic Equations