Implicit peer methods for large stiff ODE systems |
| |
Authors: | Steffen Beck Rüdiger Weiner Helmut Podhaisky Bernhard A Schmitt |
| |
Institution: | 1. Institut f??r Mathematik, Universit?t Halle, 06099, Halle, Germany 2. Fachbereich Mathematik und Informatik, Universit?t Marburg, 35032, Marburg, Germany
|
| |
Abstract: | Implicit two-step peer methods are introduced for the solution of large stiff systems. Although these methods compute s-stage approximations in each time step one-by-one like diagonally-implicit Runge-Kutta methods the order of all stages is the same due to the two-step structure. The nonlinear stage equations are solved by an inexact Newton method using the Krylov solver FOM (Arnoldi??s method). The methods are zero-stable for arbitrary step size sequences. We construct different methods having order p=s in the multi-implicit case and order p=s?1 in the singly-implicit case with arbitrary step sizes and s??5. Numerical tests in Matlab for several semi-discretized partial differential equations show the efficiency of the methods compared to other Krylov codes. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|