Convergence acceleration for the BLUES function method

2022/07/18 by Berx, Jonas
#FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2207.08632

Abstract

A detailed comparison is made between four different iterative procedures: Picard, Ishikawa, Mann and Picard-Krasnoselskii, within the framework of the BLUES function method and the variational iteration method. The resulting modified methods are subsequently applied to a nonlinear reaction-diffusion-advection differential equation to generate approximations to the known exact solution. The differences between the BLUES function method and the variational iteration method are illustrated by studying the approximants and the error between the obtained approximants and the exact solution.

Related

• Note: interpreting iterative methods convergence with diffusion point of view
• Fast convergence and asymptotic preserving of the General Synthetic Iterative Scheme
• Iterative solution of differential equations
• Numerical approximation of general Lipschitz BSDEs with branching\n processes
• Convergence Analysis of Waveform Relaxation Method to Compute Coupled Advection-Diffusion-Reaction Equations