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A new reproducing kernel Hilbert space method for solving nonlinear fourth-order boundary value problems. (English) Zbl 1166.65358

Summary: This paper presents a new reproducing kernel Hilbert space method for solving nonlinear fourth-order boundary value problems. It is a relatively new analytical technique. The solution obtained by using the method takes the form of a convergent series with easily computable components. This paper will present a numerical comparison between our method and other methods for solving an open fourth-order boundary value problem presented by M. R. Scott and H. A. Watts [SUPPORT – A computer code for two-point boundary-value problems via orthonormalization, SAND75-0198, Sandia Laboratories, Albuquerque, NM (1975)]. The method is also applied to a nonlinear fourth-order boundary value problem. The numerical results demonstrate that the new method is quite accurate and efficient for fourth-order boundary value problems.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
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