Integral-based solution for a class of second order boundary value problems

摘要

An integral formulation for the solution of a class of second order boundary value problems which are described by the equation d2yy/dx2 + P(x,y, dy/dx, d2yy/dx2)) = 0, x ε (0,a), is presented. The resulting integral equations are then solved by expressing the dependent variable y as a power series which made the computation of various integrals possible. The proposed method is tested through some examples to show the applicability of the method to solve a wide range of second order differential equations including the nonlinear ones.