A reduced computational matrix approach with convergence estimation for solving model differential equations involving specific nonlinearities of quartic type

Abstract

This study aims to efficiently solve model differential equations involving specific nonlinearities of quartictype by proposing a reduced computational matrix approach based on the generalized Mott polynomial. This methodpresents a reduced matrix expansion of the generalized Mott polynomial with the parameter-α, matrix equations,and Chebyshev–Lobatto collocation points. The simplicity of the method provides fast computation while eliminatingan algebraic system of nonlinear equations, which arises from the matrix equation. The method also scrutinizes theconsistency of the solutions due to the parameter-α. The oscillatory behavior of the obtained solutions on long timeintervals is simulated via a coupled methodology involving the proposed method and Laplace–Padé technique. Theconvergence estimation is established via residual function. Numerical and graphical results are indicated to discuss thevalidity and efficiency of the method.