The aim of this study is to obtain numerical solutions the modified Fornberg Whitham equation via collocation finite element method combined with operator splitting method. used convert original into two sub equations including linear and nonlinear part as a slight modification idea. After progress, reduce algebraic systems. For purpose, quintic B-spline base functions are polynomial approximat...

‎In this paper we introduce a numerical approach that solves optimal control problems (OCPs) ‎using collocation methods‎. ‎This approach is based upon B-spline functions‎. ‎The derivative matrices between any two families of B-spline functions are utilized to‎ ‎reduce the solution of OCPs to the solution of nonlinear optimization problems‎. ‎Numerical experiments confirm our heoretical findings‎.

We prove that the dimension of bivariate tensor–product spline spaces of bi– degree (d, d) with maximum order of smoothness on a multi–cell domain (more precisely, on a set of cells from a tensor–product grid) is equal to the number of tensor–product B–spline basis functions, defined by only single knots in both directions, acting on the considered domain. A certain reasonable assumption on the...

Simplest results presented here are the stability criteria of collocation methods for the second-order Volterra integrodifferential equation (VIDE) by polynomial spline functions. The polynomial spline collocation method is stable if all eigenvalues of a matrix are in the unit disk and all eigenvalues with |λ| = 1 belong to a 1× 1 Jordan block. Also many other conditions are derived depending u...

Application of geometric transformation to images requires an interpolation step. When applied to image rotation, the presently most e cient GPU implementation for the cubic spline image interpolation still cost about 10 times as much as linear interpolation. This implementation involves two steps: a pre lter step performs a two-pass forward-backward recursive lter, then a cubic polynomial inte...

In this paper, quadratic and sextic B-splines are used to construct an approximating function based on the integral values instead of the function values at the knots. This process due to the type of used B-splines (fourth order or sixth order), called integro quadratic or sextic spline interpolation. After introducing the integro quartic and sextic B-spline interpolation, their convergence is ...

Given a point configuration A, we uncover connection between polynomial-reproducing spline spaces over subsets of conv(A) and fine zonotopal tilings the zonotope Z(V) associated to corresponding vector configuration. This link directly generalizes known result on Delaunay configurations naturally encompasses, due its combinatorial character, case repeated affinely dependent points in A. We prov...

A previous paper described an algorithm for accurate B-spline free-form deformation of polygonal objects to produce triangular Bézier patches. However that algorithm computed the control points of resulting patches using a generalized de Casteljau algorithm, which is expensive to compute. In this short note, we describe an algorithm that instead uses polynomial interpolation; both theoretical a...

In [4] the first named author discussed the explicit solutions of the cubic spline interpolation problems. We are now concerned with quintic spline functions. Let 5B[0, n] denote the class of quintic spline functions S(x) defined in the interval [0, n] and having the points 0, 1, • • • , n — 1 as knots. This means that the restriction of S(x) to the interval (*>, J > + 1 ) (P = 0, • • • , n — \...