VARIABLE ORDER DIFFERENCE SCHEMES FOR NONLINEAR TWO-POINT BVPs
نویسندگان
چکیده
Two-point boundary value problems for a system of nonlinear first order ordinary differential equations are considered. It was shown in former papers of the authors that starting from the two-point exact difference scheme (EDS) one can derive a so-called truncated difference scheme (TDS) which possesses a prescribed order of accuracy O(|h|m) w.r.t. the maximal step size |h|. This m-TDS represents a system of nonlinear algebraic equations for the approximate values of the exact solution on the grid. In the present paper new efficient methods for the implementation of a m-TDS are discussed. Examples are given which illustrate the theorems proved in this paper. AMS classification: 65L10; 65L12; 65L20; 65L50; 34B15; 34L30
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