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

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 yiv+P(x, y, y’, y’’, y’’’) = 0, x ∈ ( 0,L), 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 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.

---

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.