New numerical scheme for solving Troesch’s Problem

Abstract

In this paper, we will manipulate the cubic spline to develop a collocation method (CSCM) and the generalized Newton method for solving the nonlinear Troesch problem. This method converges quadratically if a relation-ship between the physical parameter and the discretization parameter is satisfied. An error estimate between the exact solution and the discret solution is provided. To validate the theoretical results, Numerical results are presented and compared with other collocation methods given in the literature.

Keywords: Troesch problem, Boundary value problems, Cubic spline collocation method.