Numerical Solution of 2nd Order Boundary Value Problems with Dirichlet, Neumann and Robin Boundary Conditions using FDM

Abstract

In many fields of science and engineering, to determine the harmonic motion, damped and forced variation, current from electric circuit, 2nd order ODE is required to solve. Solving the ODE with complicated boundary condition that occur in engineering problems is a great challenges analytically. Therefore, numerical technique finite difference method (FDM) is very popular and important for solving the boundary value problems. In this article three different conditions as Dirichlet, Neumann and Robin (mixed) boundary conditions are applied in initial-boundary problem. FDM is used to solve ODE boundary value problems. Error calculation, stability, convergence are also explained. To test the accuracy numerical solutions are verified with analytical solution and error is calculated at each point for different mesh grid size as mesh grid size is decreased result will give the accuracy.