Geometric Mesh Three-Point Discretization for Fourth-Order Nonlinear Singular Differential Equations in Polar System

Abstract EN

Numerical method based on three geometric stencils has been proposed for the numerical solution of nonlinear singular fourth-order ordinary differential equations.

The method can be easily extended to the sixth-order differential equations.

Convergence analysis proves the third-order convergence of the proposed scheme.

The resulting difference equations lead to block tridiagonal matrices and can be easily solved using block Gauss-Seidel algorithm.

The computational results are provided to justify the usefulness and reliability of the proposed method.