A Sinc-Collocation Approximation Solution for Strongly Nonlinear Class of Weakly Singular Two-Point Boundary Value Problems

Abstract

In this study, an efficient collocation method based on Sinc function coupled with double exponential transformation is developed. This approach is used for solving a class of strongly nonlinear regular or weekly singular two-point BVPs with homogenous or nonhomogeneous boundary conditions. The properties of the Sinc-collocation scheme were used to reduce the computations of the problem to the nonlinear system of equations.
To use the Newton method in solving the nonlinear system, its vector-matrix form was obtained. The convergence analysis of the method is discussed. The analysis show that the method is convergent exponential.
In order to investigate the capability and accuracy of the method, it is applied to solve several existing problems chosen from the open literature. The numerical results compared with other existing methods. The
obtained results indicate high capacity and rapid convergence of the proposed method.