REPRODUCING KERNEL METHOD FOR SOLVING TENTH-ORDER BOUNDARY VALUE PROBLEMS

다국어 초록 (Multilingual Abstract)

In this paper, the tenth-order linear boundary value problems are solved using reproducing kernel method. The algorithm developed ap-proximates the solutions, and their higher-order derivatives, of differential equations and it avoids the complexity provided by other numerical ap-proaches. 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, Twiz-ell 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.

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