An innovative fourth-order numerical scheme with error analysis for Lane-Emden-Fowler type systems

In this paper, we develop a novel higher-order compact finite difference scheme for solving systems of Lane-Emden-Fowler type equations. Our method can handle these problems without needing to remove or modify the singularity. To construct the method, initially, we create a uniform mesh within the solution domain and develop a new efficient compact difference scheme. The presented method approximates the derivatives at the boundary nodal points to effectively handle the singularity. Using a matrix analysis approach, we discuss theoretical issues such as consistency, stability, and convergence. The theoretical order of the method is consistent with the numerical convergence rates. To showcase the method’s effectiveness, we apply it to solve various real-life problems from the literature and compare its performance with existing methods. The proposed method provides better numerical approximations than existing methods and offers high-order accuracy using fewer grid points.