Order reduction and how to avoid it when Lawson methods integrate\n reaction-diffusion boundary value problems

2019/09/27 by B. Cano, Cano, Begoña, Nuria Reguera +1
Engineering · Mathematics · #65M12 #65M20 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1909.12659

openalex publication_date 2019/09/27 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

It is well known that Lawson methods suffer from a severe order reduction\nwhen integrating initial boundary value problems where the solutions are not\nperiodic in space or do not satisfy enough conditions of annihilation on the\nboundary. However, in a previous paper, a modification of Lawson quadrature\nrules has been suggested so that no order reduction turns up when integrating\nlinear problems subject to even time-dependent boundary conditions. In this\npaper, we describe and thoroughly analyse a technique to avoid also order\nreduction when integrating nonlinear problems. This is very useful because,\ngiven any Runge-Kutta method of any classical order, a Lawson method can be\nconstructed associated to it for which the order is conserved.\n

Citations

• Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants
• Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems

Related

• Avoiding order reduction with explicit Runge-Kutta exponential methods in nonlinear initial boundary value problems
• Simplified explicit exponential Runge-Kutta methods without order reduction
• Avoiding order reduction when integrating diffusion-reaction boundary value problems with exponential splitting methods
• Exponential Rosenbrock methods without order reduction when integrating nonlinear initial value problems
• An Explicit Sixth Order Runge-Kutta Method for Simple Lawson Integration