The barycentric rational interpolation collocation method for boundary value problems

SPLINE COLLOCATION METHOD FOR SOLVING BOUNDARY VALUE PROBLEMS

The spline collocation method is used to approximate solutions of boundary value problems. The convergence analysis is given and the method is shown to have second-order convergence. A numerical illustration is given to show the pertinent features of the technique.  

The Linear Rational Collocation Method With Iteratively Optimized Poles for Two-Point Boundary Value Problems

Rational Spectral Collocation Method for a Coupled System of Singularly Perturbed Boundary Value Problems

A novel collocation method for a coupled system of singularly perturbed linear equations is presented. This method is based on rational spectral collocation method in barycentric form with sinh transform. By sinh transform, the original Chebyshev points are mapped into the transformed ones clustered near the singular points of the solution. The results from asymptotic analysis about the singula...

Weighted radial basis collocation method for boundary value problems

This work introduces the weighted radial basis collocation method for boundary value problems. We first show that the employment of least-squares functional with quadrature rules constitutes an approximation of the direct collocation method. Standard radial basis collocation method, however, yields a larger solution error near boundaries. The residuals in the least-squares functional associated...

A Collocation Method for Linear Fourth Order Boundary Value Problems

We propose and analyze a numerical method for solving fourth order differential equations modelling two point boundary value problems. The scheme is based on B-splines collocation. The error analysis is carried out and convergence rates are derived.