The collocation methods based on cubic B-spline, are developed to approximate solution of the second and first kind Fredholm integral equations.First we collocate the solution by B-spline and the Newton-Cotes formula is used to approximate integral. Convergence analysis has been investigated and proved that the quadratur rule is fourth order convergent. The presented methods are tested to the p...

Collocation methods based on quartic splines are presented for second-order two-point boundary value problems. In order to obtain a uniquely solvable linear system for the degrees of freedom of the quartic spline collocation approximation, in addition to the boundary conditions specified by the problem, extra boundary or near-boundary conditions are introduced. Non-optimal (fourth-order) and op...

We consider solitary wave solutions of the generalized equal width (GEW) wave equation ut + εuux − δuxxt = 0. This paper presents a collocation method for the GEW equation, which is classified as a nonlinear PDE using quadratic B-splines at midpoints as element shape functions. In this research, the scheme of the equation under investigation is found to be unconditionally stable. Test problems ...

Quartic-Spline Collocation Methods for Fourth-Order Two-Point Boundary Value Problems Ying Zhu Master of Science Graduate Department of Computer Science University of Toronto 2001 This thesis presents numerical methods for the solution of general linear fourth-order boundary value problems in one dimension. The methods are based on quartic splines, that is, piecewise quartic polynomials with C3...

A collocation procedure is developed for the linear and nonlinear Fredholm and Volterra integro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. Numerical results are given t...

Tension spline is a function that, for given partition x0 < x1 < . . . < xn, on each interval [xi, xi+1] satisfies differential equation (D − ρiD)u = 0, where ρi’s are prescribed nonnegative real numbers. In the literature, tension splines are used in collocation methods applied to two-points singularly perturbed boundary value problems with Dirichlet boundary conditions. In this paper, we adap...

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...

We formulate new optimal quadratic spline collocation methods for the solution of various elliptic boundary value problems in the unit square. These methods are constructed so that the collocation equations can be solved using a matrix decomposition algorithm. The results of numerical experiments exhibit the expected optimal global accuracy as well as superconvergence phenomena. AMS subject cla...

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