A Second Order Non-uniform Mesh Discretization for the Numerical Treatment of Singular Two-Point Boundary Value Problems with Integral Forcing Function

摘要

In the present work, we examine the three-point numerical scheme for the non-linear second order ordinary differential equations having integral form of forcing function. The approximations of solution values are obtained by means of finite difference scheme based on a special type of non-uniform meshes. The derivatives as well as integrals are approximated with simple second order accuracy both on uniform meshes and non-uniform meshes. A brief convergence analysis based on irreducible and monotone behaviour of Jacobian matrix to the numerical scheme is provided. The scheme is then tested on linear and non-linear examples that justify the order and accuracy of the new method.