Numerical Simulation of a Non-linear Singular Perturbed Schrödinger Equation Using Finite Element Approximation

This paper is concerned with the various finite element solutions of non-linear singularly perturbed Schrödinger boundary value problems. Non-linear Schrödinger equation does not appear to have been previously studied in detail computationally and it is hope that this paper will help to provide a new idea in this direction. To linearize the nonlinear system of equations, we introduced a concept of new modified fifth order Newton type iterative method and discussed the behavior of the solution. In order to confirm our theoretical results, numerically and to demonstrate the performance of the proposed algorithm, we have considered two examples of non-linear Schrödinger’s equation involving non-linearity in homogenous and non-homogenous form.