31,773 research outputs found
High order semi-implicit schemes for time dependent partial differential equations
International audienceThe main purpose of the paper is to show how to use implicit-explicit (IMEX) Runge- Kutta methods in a much more general context than usually found in the literature, obtaining very effective schemes for a large class of problems. This approach gives a great flexibility, and allows, in many cases the construction of simple linearly implicit schemes without any Newton’s iteration. This is obtained by identifying the (possibly linear) dependence on the unknown of the system which generates the stiffness. Only the stiff dependence is treated implicitly, then making the whole method much simpler than fully implicit ones. The resulting schemes are denoted as semi-implicit R-K. We adopt several semi-implicit R-K methods up to order three. We illustrate the effectiveness of the new approach with many applications to reaction-diffusion, convection diffusion and nonlinear diffusion system of equations
Construction of additive semi-implicit Runge-Kutta methods with low-storage requirements
The final publication is available at Springer via
http://dx.doi.org/ 10.1007/s10915-015-0116-2Space discretization of some time-dependent partial differential equations gives rise to systems of
ordinary differential equations in additive form whose terms have different stiffness properties. In these
cases, implicit methods should be used to integrate the stiff terms while efficient explicit methods can be
used for the non-stiff part of the problem. However, for systems with a large number of equations, memory
storage requirement is also an important issue. When the high dimension of the problem compromises
the computer memory capacity, it is important to incorporate low memory usage to some other properties of the scheme.
In this paper we consider Additive Semi-Implicit Runge-Kutta (ASIRK) methods, a class of implicitexplicit
Runge-Kutta methods for additive differential systems. We construct two second order 3-stage
ASIRK schemes with low-storage requirements. Having in mind problems with stiffness parameters,
besides accuracy and stability properties, we also impose stiff accuracy conditions. The numerical experiments done show the advantages of the new methods.Supported by Ministerio de EconomĂa y Competividad, project MTM2011-23203
- …