An adaptive multiresolution scheme with second order local time-stepping for reaction-diffusion equations

Abstract

Listen

Translate article

For adaptive multiresolution schemes we propose a local time stepping scheme based on natural extensions of Runge-Kutta methods. We consider reaction-diffusion equations in two space dimensions and assess the precision and efficiency of the new method. The obtained results are compared with those using classical finite volume schemes on a uniform grid and multiresolution schemes with global time stepping. It is shown that both CPU time and precision of the adaptive solutions are improved.