A Numerical Solution to the Nonlinear Fifth Order Boundary Value Problems
نویسندگان
چکیده
Fifth order boundary value problem appears in the mathematical modelling of viscoelastic flows and other branches of mathematical, physical and engineering sciences [4, 5]. The conditions for the existence and uniqueness of the solution of such problems can be found in [6]. Gamel [2] analyzed Sinc-Galerkin method for the solution of fifth-order boundary value problems with two-point boundary conditions. Shen [3] solved fifth-order boundary value problems using the homotopy perturbation method. Siddiqi and Ghazala presented nonpolynomial spline method [7], polynomial sextic spline method [8] for the numerical solution of the fifth-order linear special case boundary value problems and the method is observed to be second-order convergent. Ghazala and Hamood [1] developed searching the least value (SLV) method for the solution of fifth order boundary value problem. In this paper, a reproducing kernel method is used for the solution of nonlinear fifth order boundary value problem. The method discussed in this paper also applied to solve general fifth order boundary value problem. To the best of our knowledge, such boundary value problem involving ) x ( u ), x ( u ), x ( u ), x ( u ) 2 ( ) 3 ( ) 4 ( ) 5 ( has not been already solved. The following fifth order nonlinear boundary value problem (BVP) can be considered as
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