Efficient sixth order methods for nonlinear oscillation problems |
| |
Authors: | R M Thomas |
| |
Institution: | (1) Department of Mathematics, UMIST, P.O. Box 88, M60 1QD Manchester, United Kingdom |
| |
Abstract: | A class of two-step (hybrid) methods is considered for solving pure oscillation second order initial value problems. The nonlinear system, which results on applying methods of this type to a nonlinear differential system, may be solved using a modified Newton iteration scheme. From this class the author has derived methods which are fourth order accurate,P-stable, require only two (new) function evaluations per iteration and have a true real perfect square iteration matrix. Now, we propose an extension to sixth order,P-stable methods which require only three (new) function evaluations per iteration and for which the iteration matrix is a true realperfect cube. This implies that at most one real matrix must be factorised at each step. These methods have been implemented in a new variable step, local error controlling code. |
| |
Keywords: | AMS 65L05 |
本文献已被 SpringerLink 等数据库收录! |
|