%0 Journal Article
%A Martín-Vaquero, J.
%A Kleefeld, Andreas
%T ESERK5: A fifth-order extrapolated stabilized explicit Runge–Kutta method
%J Journal of computational and applied mathematics
%V 356
%@ 0377-0427
%C Amsterdam
%I North-Holland
%M FZJ-2019-01365
%P 22-36
%D 2019
%X A new algorithm is developed and analyzed for multi-dimensional non-linear parabolic partial differential equations (PDEs) which are semi-discretized in the spatial variables leading to a system of ordinary differential equations (ODEs). It is based on fifth-order extrapolated stabilized explicit Runge–Kutta schemes (ESERK). They are explicit methods, and therefore it is not necessary to employ complicated software for linear or non-linear system of equations. Additionally, they have extended stability regions along the negative real semi-axis, hence they can be considered to solve stiff problems coming from very common diffusion or reaction–diffusion problems.Previously, only lower-order codes (up to fourth-order) have been constructed and made available in the scientific literature. However, at the same time, higher-order codes were demonstrated to be very efficient to solve equations where it is necessary to have a high precision or they have transient zones that are very severe, and where functions change very fast. The new schemes allow changing the step length very easily and with a very small computational cost. Thus, a variable step length, with variable number of stages algorithm is constructed and compared with good numerical results in relation to other well-known ODE solvers.
%F PUB:(DE-HGF)16
%9 Journal Article
%U <Go to ISI:>//WOS:000463693100002
%R 10.1016/j.cam.2019.01.040
%U https://juser.fz-juelich.de/record/860700