High order methods for the numerical solution of two-point boundary value problems |
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Authors: | J. R. Cash A. Singhal |
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Affiliation: | (1) Department of Mathematics, Imperial College, South Kensington, London S.W.7, England |
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Abstract: | In a recent paper, Cash and Moore have given a fourth order formula for the approximate numerical integration of two-point boundary value problems in O.D.E.s. The formula presented was in effect a one-off formula in that it was obtained using a trial and error approach. The purpose of the present paper is to describe a unified approach to the derivation of high order formulae for the numerical integration of two-point boundary value problems. It is shown that the formula derived by Cash and Moore fits naturally into this framework and some new formulae of orders 4, 6 and 8 are derived using this approach. A numerical comparison with certain existing finite difference methods is made and this comparison indicates the efficiency of the high order methods for problems having a suitably smooth solution. |
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