NOVEL EXACT AND APPROXIMATE SOLUTIONS OF THE NEWELL-WHITEHEAD-SEGEL TYPE EQUATIONS

The main goal of this study is to find different and new analytical and numerical solutions of the Newell-Whitehead-Segel-type equations, which belong to the most consequential amplitude equations in physical phenomena, such as fluid mechanics, solid-state physics, optics, plasma physics, dispersion, and chemical kinetics. To address the inherent complexities associated with the nonlinear equation, the researchers employed highly effective techniques: the novel -expansion method and the septic B-spline collocation method. The error norms and are calculated for the adequacy and efficiency of the present method. The method’s unconditional stability is demonstrated through the use of von-Neumann stability analysis. The appropriate solutions for the three test problems are found by computing the and error norms, which highlight the significance of the procedure and demonstrate its applicability and credibility. The inferred numerical results show good agreement with the analytical solutions, indicating that the current B-spline collocation approach is a robust and attractive algorithm. The results are tabulated and reported both modally and in terms of the productivity of the procedure. The results produced from both analytical and numerical methods demonstrate the great utility of this study for scientists tasked with identifying characteristics and features of nonlinear processes across a variety of scientific domains.