Rational collocation for linear 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

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.

An ${cal O}(h^{8})$ optimal B-spline collocation for solving higher order boundary value problems

As we know the approximation solution of seventh order two points boundary value problems based on B-spline of degree eight has only ${cal O}(h^{2})$ accuracy and this approximation is non-optimal. In this work, we obtain an optimal spline collocation method for solving the general nonlinear seventh order two points boundary value problems. The ${cal O}(h^{8})$ convergence analysis, mainly base...

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...