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REPRODUCING KERNEL METHOD FOR SOLVING TENTH-ORDER BOUNDARY VALUE PROBLEMS  

Geng, Fazhan (Department of Mathematics, Changshu Institute of Technology)
Cui, Minggen (Department of Mathematics, Harbin Institute of Technology)
Publication Information
Journal of applied mathematics & informatics / v.28, no.3_4, 2010 , pp. 813-821 More about this Journal
Abstract
In this paper, the tenth-order linear boundary value problems are solved using reproducing kernel method. The algorithm developed approximates the solutions, and their higher-order derivatives, of differential equations and it avoids the complexity provided by other numerical approaches. First a new reproducing kernel space is constructed to solve this class of tenth-order linear boundary value problems; then the approximate solutions of such problems are given in the form of series using the present method. Three examples compared with those considered by Siddiqi, Twizell and Akram [S.S. Siddiqi, E.H. Twizell, Spline solutions of linear tenth order boundary value problems, Int. J. Comput. Math. 68 (1998) 345-362; S.S.Siddiqi, G.Akram, Solutions of tenth-order boundary value problems using eleventh degree spline, Applied Mathematics and Computation 185 (1)(2007) 115-127] show that the method developed in this paper is more efficient.
Keywords
Tenth-order; boundary value problems; reproducing kernel method;
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Times Cited By KSCI : 1  (Citation Analysis)
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