B-Spline Method for Two-Point Boundary Value Problems
نویسنده
چکیده
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 2014, Accepted: 23 June 2014.
منابع مشابه
B-SPLINE METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEMS
In this work the collocation method based on quartic B-spline is developed and applied to two-point boundary value problem in ordinary diferential 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.
متن کاملNON-POLYNOMIAL SPLINE SOLUTIONS FOR SPECIAL NONLINEAR FOURTH-ORDER BOUNDARY VALUE PROBLEMS
We present a sixth-order non-polynomial spline method for the solutions of two-point nonlinear boundary value problem u(4)+f(x,u)=0, u(a)=α1, u''(a)= α2, u(b)= β1,u''(b)= β2, in off step points. Numerical method of sixth-order with end conditions of the order 6 is derived. The convergence analysis of the method has been discussed. Numerical examples are presented to illustrate the applications ...
متن کاملAn ${cal O}(h^{8})$ 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...
متن کاملB-Spline Finite Element Method for Solving Linear System of Second-Order Boundary Value Problems
In this paper, we solve a linear system of second-order boundary value problems by using the quadratic B-spline nite el- ement method (FEM). The performance of the method is tested on one model problem. Comparisons are made with both the analyti- cal solution and some recent results.The obtained numerical results show that the method is ecient.
متن کاملNUMERICAL SOLUTIONS OF SECOND ORDER BOUNDARY VALUE PROBLEM BY USING HYPERBOLIC UNIFORM B-SPLINES OF ORDER 4
In this paper, using the hyperbolic uniform spline of order 4 we develop the classes of methods for the numerical solution of second order boundary value problems (2VBP) with Dirichlet, Neumann and Cauchy types boundary conditions. The second derivativeis approximated by the three-point central difference scheme. The approximate results, obtained by the proposed method, confirm theconvergence o...
متن کاملSPLINE 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.
متن کامل