On the dynamical behavior of nonlinear Fitzhugh–Nagumo and Bateman–Burger equations in quantum model using Sinc collocation scheme

The main objective of this study is to numerically investigate the dynamical behavior of nonlinear Fitzhugh–Nagumo and Bateman–Burger systems through the Sinc collocation method by means of the θ-weighted scheme on various grid points of time-dependent evolutionary one spatial dimension in open quantum flow field model. The proposed technique based on the Sinc function is treated as a shape function to transform the governing nonlinear partial differential equation into an algebraic system. To approximate the time and spatial derivatives, finite difference scheme and the θ-weighted scheme have been used simultaneously due to the occurrence of infinite domain and multiple singularities. The effectiveness of the proposed results on the computational ground is illustrated graphically for better understanding and reliable performance of the design scheme is endorsed based on assessments of achieved accuracy in terms of stability analysis and convergence analysis.