Lobatto-Obrechkoff Formulae for 2nd Order Two-Point Boundary Value Problems

Date of Online Publication: 26/08/2006
Keywords: MIRK, Runge Kutta, ODE, Boundary Value Problem, Lobatto Formulae, Obrechkoff Formulae
Authors: S. D. Capper, J. R. Cash and D. R. Moore
Pages: 13-25
A substantial increase in efficiency may be obtained by numerical integration methods which take advantage of the special second order forms or in systems of second order two-point boundary value problems, while retaining the MIRK structure. In particular, for these special second order equations, we derive high order methods which require considerably fewer function evaluations than are required by methods intended for general first order systems. Methods based on a Lobatto-MIRK formula for finding and an Obrechkoff type formula for finding using the same values of are derived and these methods are of sixth and of eighth order accuracy.

 

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