Numerical solution of linear second order ordinary differential equations with mixed boundary conditions by galerkin method

Abstract

The purpose of this study was to find numerical solutions of linear second order ordinary differential equations with mixed boundary condition by Galerkin method using Chebyshev polynomial as a trial function. The Galerkin method was applied after converting the given linear second order ordinary differential equation with mixed boundary condition into equivalent boundary value problem by considering a valid assumption for the independent variable and also converting mixed boundary condition in to Neumann type. The resulting system of equation was solved by direct method. In order to check to what extent our method approximates the exact solution, a test example with known exact solution was solved and compared with the exact solution graphically as well as numerically.