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.  

A quadratic non-polynomial spline functions based method is developed to find approximations solution to a system of second-order boundary-value problems associated with obstacle, unilateral, and contact problems. The present approach has less computational cost and gives better approximations than those produced by other collocation, finite-difference and spline methods. Convergence analysis o...

A collocation method based on modified cubic B-spline functions has been developed for the valuation of European, American and barrier options of a single asset. The new approach contains discretization of temporal derivative using finite difference approximation of and approximating the option price with the modified B-spline functions. Stability of this method has been discussed and it is sho...

A B-spline collocation method is developed for solving boundary value problems which arise from the problems of calculus of variations. Some properties of the B-spline procedure required for subsequent development are given, and they are utilized to reduce the solution computation of boundary value problems to some algebraic equations. The method is applied to a few test examples to illustrate ...

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 ...

Simple geometric proofs are given for the total positivity of the B-spline collocation matrix and the variation diminishing property of the B-spline representation of a spline.

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...

In the work of solving a uniformly elliptic differential equations Au := − u+ a1ux + a2uy + a0u = f in the unit square with boundary conditions by the C1-cubic spline collocation method, one may need to investigate efficient preconditioning techniques. For this purpose, using the generalized field of values argument, we show the uniform bounds of the eigenvalues of the preconditioned matrix whe...

The present paper uses new approach and methodology to solve second order one dimensional hyperbolic telegraph equation numerically by B-spline collocation method. It is based on collocation of modified cubic B-spline basis functions over the finite elements. The given equation is decomposed into system of equations and modified cubic B-spline basis functions have been used for spatial variable...

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...