RT info:eu-repo/semantics/article T1 Generalized TASE-RK methods for stiff problems A1 Hernández Abreu, Domingo A1 Gonz´alez Pinto A1 Pagano, G. A1 P´erez Rodr´ıguez, S. A2 Análisis Matemático A2 Grupo de investigación ULL: "Métodos numéricos en ecuaciones diferenciales" https://www.ull.es/grupoinvestigacion/met-numericos-ec-diferenciales/ K1 Explicit Runge-Kutta methods K1 TASE-RK methods K1 W-methods K1 Rosenbrock methods K1 Time Integration K1 Stability K1 Stiffness AB A family of Time-Accurate and Stable Explicit (TASE) methods for the numerical integration of Initial Value Problems in stiff Ordinary Differential Equations (ODEs) y ′(t) = f(t, y) was recently introduced in [1]. The main idea was to make local extrapolation of a stabilized Euler method. More recently, in [3] a similar approach by considering the stabilization of arbitrary explicit Runge-Kutta methods (TASE-RK) was analyzed. In this case the explicit Runge-Kutta method integrates a transformed ODE obtained by multiplying the vector field f(t, y) by a certain operator which approximates the identity mapping up to a given order p. The main inconvenience of both approaches is that to reach order p the solution of p2linear systems plus the evaluation of p derivatives are required per integration step.In order to substantially reduce the computational costs of the former approaches in the linear system solution, but maintaining the good accuracy and stability properties, a new family of TASE-RK methods which allow to introduce a few more free parameters are considered. The formulation of the methods was conceived to be implemented not only in sequential mode but it admits parallelism in a straigthforward way. Furthermore, since these methods are linearly implicit, connections to the class of W-methods [19] are properly established. The order conditions for the new class of methods are widely studied by usingthe rooted tree theory. For p = 3, 4, new methods with p sequential stages and order p are derived and compared on semidiscrete 1D and 2D Partial Differential Equations (PDEs) to those in [1, 3] and other standard Rosenbrock and W-methods in the literature. YR 2023 FD 2023 LK http://riull.ull.es/xmlui/handle/915/39027 UL http://riull.ull.es/xmlui/handle/915/39027 LA en DS Repositorio institucional de la Universidad de La Laguna RD 24-nov-2024