Numerical Tests of Novel Finite Difference Operator for Solving 1D Boundary-Value Problems

The finite-difference method is an important approach for solving boundary-value problems of nonlinear ordinary and partial differential equations. In this approach, derivatives and partial derivatives are substituted by discrete finite-difference operators by considering the values at adjacent points, and finite-difference algebraic equations are developed. A large class of discrete operators exists and has been presented in many books on numerical methods. In the present study, an alternative approach to solving boundary-value problems is presented, which can be classified to a group of finite-difference methods.