Geometric mesh three-point discretization for fourth-order nonlinear singular differential equations in polar system (Q2248684)

Summary: A numerical method based on three geometric stencils is proposed for the numerical solution of nonlinear singular fourth-order ordinary differential equations. The method can be easily extended to sixth-order differential equations. A 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.