Implementing a seventh-order linear multistep method in a predictor-corrector mode or block mode: which is more efficient for the general second order initial value problem

Samuel N Jator; Leong Lee

doi:10.1186/2193-1801-3-447

Implementing a seventh-order linear multistep method in a predictor-corrector mode or block mode: which is more efficient for the general second order initial value problem

Springerplus. 2014 Aug 20:3:447. doi: 10.1186/2193-1801-3-447. eCollection 2014.

Authors

Samuel N Jator¹, Leong Lee²

Affiliations

¹ Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044 USA.
² Department of Computer Science and Information Technology, Austin Peay State University, Clarksville, TN 37044 USA.

Abstract

A Seventh-Order Linear Multistep Method (SOLMM) is developed and implemented in both predictor-corrector mode and block mode. The two approaches are compared by measuring their total number of function evaluations and CPU times. The stability property of the method is examined. This SOLMM is also compared with existing methods in the literature using standard numerical examples.

Ams subject classification: 65L05; 65L06.

Keywords: General second order; Initial value problems; Block form.