Symmetric implicit multiderivative numerical integrators for direct solution of fifth-order differential equations

Abstract

Abstract

A direct method of solution of fifth order ordinary differential equations (odes) is proposed in this paper. Collocation of the differential system is taken at selected grid points to reduce the number of functions to be evaluated per iteration. A number of predictors of the same order of accuracy with the main method for the estimation of -functions and their derivatives in the main method are generated. The symmetric implicit multiderivative algorithm [SIMA] is suitable for numerical integration of non-stiff and mildly-stiff fifth order equations. Test examples are solved with the method to confirm its efficiency.

Keywords: Symmetric; multiderivative; implicit; interval of absolute stability; error constant.