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Boundary integral solution for a class of fourth-order two-point boundary value problems

Husain J. Al-Gahtani
2016 Journal of Applied Mathematics and Computational Mechanics  
In this paper, a boundary integral method is proposed for the solution of a class of fourth-order two-boundary value problems described by the equation ‫ݕ‬ ௩ + ܲሺ‫,ݔ‬ ‫,ݕ‬ ‫ݕ‬ ᇱ , ‫ݕ‬ ᇱᇱ , ‫ݕ‬ ᇱᇱᇱ ሻ = 0, ‫ݔ‬ ∈ ሺ0, ‫ܮ‬ሻ, where P is a polynomial function of its arguments. The differential equation is cast in an integral form and the weighted residual technique is used to generate the corresponding boundary integral equations. The boundary integral equations are then, solved by expressing the
more » ... expressing the dependent variable, y, in terms of a power series. The proposed method is tested through four examples to show the applicability of the method to solve a wide range of fourth-order differential equations including the nonlinear ones.
doi:10.17512/jamcm.2016.3.01 fatcat:g62h3on26rhmlpeugsucu6tpsu