Biorthogonal flatlet multiwavelet collocation method for solving the singular nonlinear system with initial and boundary conditions

Abstract

Purpose

The numerical methods are of great importance for approximating the solutions of a system of nonlinear singular ordinary differential equations. In this paper, the authors present the biorthogonal flatlet multiwavelet collocation method (BFMCM) as a numerical scheme for a class of system of Lane–Emden equations with initial or boundary or four-point boundary conditions.

Design/methodology/approach

The approach is involved in combining the biorthogonal flatlet multiwavelet (BFM) with the collocation method. The authors investigate the properties and procedure of the BFMCM for first time on this class of equations. By using the BFM and the collocation points, the method is constructed and it transforms the nonlinear differential equations problem into a system of nonlinear algebraic equations. The unknown coefficients of the assuming solution are determined by solving the obtained system. Additionally, convergence analysis and numerical stability of the suggested method are provided.

Findings

According to the attained results, the proposed BFMCM has more accurate results in comparison with results of other methods. The maximum absolute errors are calculated by using the BFMCM for comparison purposes provided.

Originality/value

The key desirable properties of BFMCM are its efficiency, simple applicability and minimizes errors. Therefore, the proposed method can be used to solve nonlinear problems or problems with singular points.

Citation

Mohseni, M. and Rostamy, D. (2023), "Biorthogonal flatlet multiwavelet collocation method for solving the singular nonlinear system with initial and boundary conditions", Engineering Computations, Vol. 40 No. 9/10, pp. 2533-2557. https://doi.org/10.1108/EC-12-2022-0730