A discontinuous Galerkin finite element method for solving the Troesch's problem

In this paper we propose a new discontinuous Galerkin finite element (DG) method to solve Troesch's problem, which is highly sensitive for large values of the parameter. This two-point boundary value problem has been heavily studied since 1960, however, only a few papers have provided a reliable solution for high sensitivity. Therefore, we developed the DG method which has proved its efficiency for many decades to be a new numerical solver. We demonstrate through computational results compared with those computed by other methods, that the discontinuous Galerkin method provides a quite efficient, accurate and reliable solution. Thus, the DG method is an attractive and competitive alternative to other numerical and semi-analytical techniques to solve highly sensitive nonlinear problems.