Solving Two-Point Second Order Boundary Value Problems Using Two-Step Block Method with Starting and Non-Starting Values

摘要

Second order boundary value problems can be solved directly using block methods. This solution can be implemented with or without the use of starting values. However, a comparison of the effects of starting values on the results gotten from solving a second order boundary value problem has not been investigated into. Therefore, in this work a two-step block method for the numerical solution of a two-point second order boundary value problem is described. The derivation of the method from Taylor series expansions leads to a family of block matrix equations which are used to solve the boundary value problems. The method is implemented with starting and non-starting values and the results are compared with previously existing methods. The results show an improvement in the accuracy of the method when implemented with starting values.