An Adaptive Multiresolution Scheme with Second Order Local Time-stepping for Reaction-diffusion Equations - Lopes, Müller Moreira; Domingues, Margarete O.; Mendes, Odim; Schneider, Kai (Journal of Applied Nonlinear Dynamics, 2026)
For adaptive multiresolution schemes we propose a local timestepping 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.