Keywords : Runge-Kutta methods

Numerical Stability Study of the Explicit-Implicit Range-Kuta Synthesis Methods (IMEX-ARK)

Thair Y. Thanoon; Younis Abd Hussain

AL-Rafidain Journal of Computer Sciences and Mathematics, 2010, Volume 7, Issue 1, Pages 13-27
DOI: 10.33899/csmj.2010.163861

In this research we studied the numerical stability for Implicit-Explicit Additive Runge-Kutta (IMEX-ARK) methods which have the          A[]-stability .This stability is equivalent A-stability of (B()-ARK) methods where B()=B1+(1-)B2 of second and third order for different intervals of values.This methods are suitable for solving stiff non-linear differential equations which has the form :
which contains stiff and non-stiff terms. We have used Matlab as programming tool .

Parallel Implicit Runge-Kutta Methods for Stiff ODEs

Bashir M. S. Khalaf; Abdulhabib A. A. Murshid

AL-Rafidain Journal of Computer Sciences and Mathematics, 2004, Volume 1, Issue 2, Pages 79-106
DOI: 10.33899/csmj.2004.164113

The main objective of this paper is to develop and construct numerical algorithms for solving stiff system of ordinary differential equations (ODEs) which are suitable for running on parallel computers (MIMD computers).Semi-parallel implicit Runge-Kutta methods have been derived and parallel predictor - corrector methods are developed.