Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4646020 | Applied Numerical Mathematics | 2009 | 8 Pages |
Abstract
The boundary value problem (BVP) for a scalar nonlinear second order differential equation on the half-axis is considered. A constructive method is proposed to derive from the three-point exact difference scheme (EDS) a so-called truncated difference scheme (n-TDS) of rank n, where n is a freely chosen natural number. The n-TDS has the order of accuracy , i.e., the global error is of the form , where |h| is the maximum step size and denotes the entire part of the expression in brackets. This n-TDS is the basis for a new adaptive algorithm which has all the advantages known from the modern IVP-solvers. Numerical examples are given which confirm the efficiency and reliability of our algorithm.
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