Three point discretization of order four and six for (du:dx) of the solution of non-linear singular two point boundary value problem

Abstract

We present finite difference methods of order four and six for the numerical solution of (du/dx) for the non-linear differential equation u″ = f(x,u,u′), 0 < x > 1 subject to the boundary conditions u(0) = A, u(l) =B. The proposed methods require only three grid points and applicable to both singular and non-singular problems. Numerical examples are given to illustrate the methods and their convergence.

Keywords:

• Finite difference methods
• Non-linear equation
• Local truncation error
• Singular equation
• First order derivative
• Burger's equation
• RMS errors

C.R. Categories:

• G.1.7

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