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.
