New algorithms for the numerical solution of one dimensional singular biharmonic problems of second kind

Abstract

We derive two new finite difference methods of order two and four usingthree grid points for solving the general one dimensional nonlinear biharmonic equation subject to the boundary conditions .Second order derivative of the solution are obtained as a by-product of the methods and we do not require to discretize the boundary conditions. We also discuss fourth order difference method for a fourth order linear differential equation in cylindrical and spherical symmetry. The resulting matrix system is solved by the non-linear block successive over relaxation (NBSOR) method. In numerical experiments the new second and fourth order methods are compared with the exact solutions both in singular and non-singular cases.

Keywords:

• Finite difference method
• nonlinear biharmonic equation
• singular equation
• cylindrical and spherical symmetry
• NBSOR method
• BSOR method

C.R. Category:

• G.1.7