In this work the collocation method based on quartic B-spline is developed and applied to two-point boundary value problem in ordinary differential equations. The error analysis and convergence of presented method is discussed. The method illustrated by two test examples which verify that the presented method is applicable and considerable accurate. Received: 2 February 2014, Revised: 4 May 201...

A collocation-Galerkin scheme is proposed for an initial-boundary value problem for a first order hyperbolic equation in one space dimension. The Galerkin equations satisfied by the approximating solution are obtained from a weak-weak formulation of the initial-boundary value problem. The collocation points are taken to be affine images of the roots of the Jacobian polynomials of degree r — \ o...

A collocation method for approximating integrals of rapidly oscillatory functions is analyzed. The method is efficient for integrals involving Bessel functions J,.(rx) with a large oscillation frequency parameter r, as well as for many other oneand multi-dimensional integrals of functions with rapid irregular oscillations. The analysis provides a convergence rate and it shows that the relative ...

In this paper we are concerned with the numerical analysis of the collocation method based on graded meshes of second kind integral equations on the real line of the form φ(s)=ψ(s)+ ∫ R κ(s − t)z(t)φ(t) dt, s ∈R, where κ ∈ L1(R), z ∈ L∞(R), and ψ ∈ BC(R), the space of bounded continuous complex-valued functions on R, are assumed known and the function φ ∈ BC(R) is to be determined. We introduce...

here a posteriori error estimate for the numerical solution of nonlinear voltena- hammerstein equations is given. we present an error upper bound for nonlinear voltena-hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of brunner for these problems (the implicitly linear collocation method).we al...

Nowadays, spaceborne Synthetic Aperture Radar (SAR) has become a powerful tool for providing significant wave height (SWH). Traditionally, validation of SAR derived SWH has been carried out against buoy measurements or model outputs, which only yield an inter-comparison, but not an “absolute” validation. In this study, the triple collocation error model has been introduced in the validation of ...

This paper is concerned with the application of boundary integral equation method to the electromagnetic scattering of a perfect conductor in the three dimensional space. A collocation method is employed for the magnetic eld integral equation and error estimates are derived. Fareld patterns and radar cross sections are computed for various wave numbers in the case of sphere. Numerical experimen...

Nowadays, spaceborne Synthetic Aperture Radar (SAR) has become a powerful tool for providing significant wave height. Traditionally, validation of SAR derived ocean wave height has been carried out against buoy measurements or model outputs, which only yield a inter-comparison, but not an ‘absolute’ validation. In this study, the triple collocation error model has been introduced in the validat...

We present in this paper the convergence properties of Jacobi spectral collocation method when used to approximate the solution of multidimensional nonlinear Volterra integral equation. The solution is sufficiently smooth while the source function and the kernel function are smooth. We choose the Jacobi-Gauss points associated with the multidimensional Jacobi weight function [Formula: see text]...

The Cahn–Hilliard equation plays an important role in the phase separation in a binary mixture. This is a fourth order nonlinear partial differential equation. In this paper, we study the behaviour of the solution by using orthogonal cubic spline collocation method and derive optimal order error estimates. We discuss some computational experiments by using monomial basis functions in the spatia...