Detecting Inverse Boundaries by Weighted High-Order Gradient Collocation Method

A numerical approach to solve eighth order boundary value problems by Haar wavelet collocation method

In this paper a robust and accurate algorithm based on Haar wavelet collocation method (HWCM) is proposed for solving eighth order boundary value problems. We used the Haar direct method for calculating multiple integrals of Haar functions. To illustrate the efficiency and accuracy of the concerned method, few examples are considered which arise in the mathematical modeling of fluid dynamics an...

A collocation method for high frequency scattering by convex polygons

We consider the problem of scattering of a time-harmonic acoustic incident plane wave by a sound soft convex polygon. Standard boundary or finite element methods, with a piecewise polynomial approximation space, have a computational cost that grows linearly with respect to the frequency of the incident wave. Recently ChandlerWilde and Langdon proposed a novel Galerkin boundary element method fo...

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 Method for Defuzzication by Weighted Distance

Numerical Solution of Fifth Order Boundary Value Problems by Collocation Method with Sixth Order B-Splines

Collocation method with sixth degree B-splines as basis functions has been developed to solve a fifth order special case boundary value problem. To get an accurate solution by the collocation method with sixth degree B-splines, the original sixth degree B-splines are redefined into a new set of basis functions which in number match with the number of collocation points. The method is tested for...