## Difference schemes for nonlinear BVPs using Runge-Kutta IVP-solvers.(English)Zbl 1139.65057

Summary: Difference schemes for two-point boundary value problems for systems of first-order nonlinear 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 a priori possesses an arbitrary given order of accuracy $${\mathcal O}(|h|^m)$$ with respect to 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 he present paper, new efficient methods for the implementation of an $$m$$-TDS are discussed. Examples are given which illustrate the theorems proved in this paper.

### MSC:

 65L12 Finite difference and finite volume methods for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 65L10 Numerical solution of boundary value problems involving ordinary differential equations

RWPM
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### References:

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