Numerical solutions of Schrödinger wave equation and Transport equation through Sinc collocation method

This study carries the novel applications of the Sinc collocation method to investigate the numerical computing paradigm of Schrödinger wave equation and Transport equation as a great level of accuracy and precision. A global collocation-based Sinc function is embedded with a cardinal expansion to discretize initially time derivatives by finite difference method and secondly spatial derivatives are approximated with θ-weighted scheme. Sinc collocation method (SCM) is found to be a more robust approach in order to avoid singularities in proposed problems and for yielding accurate numerical results. The governing PDEs are transformed with the help of Sinc function into algebraic system of equations, and further, these algebraic equations are solved with the help of computational iteration scheme to obtain the numerical results. The scheme provides a reliable and excellent procedure for adaptation of finding unknown in Sinc function for these problems. An extensive stability analysis is done to validate the convergence, accuracy and exactness of the proposed scheme.