TY  - JOUR
AU  - Martín-Vaquero, J.
AU  - Kleefeld, Andreas
TI  - ESERK5: A fifth-order extrapolated stabilized explicit Runge–Kutta method
JO  - Journal of computational and applied mathematics
VL  - 356
SN  - 0377-0427
CY  - Amsterdam
PB  - North-Holland
M1  - FZJ-2019-01365
SP  - 22-36
PY  - 2019
AB  - 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000463693100002
DO  - DOI:10.1016/j.cam.2019.01.040
UR  - https://juser.fz-juelich.de/record/860700
ER  -