By applying finite difference formula to time discretization and the cubic B-splines for spatial variable, a numerical method for solving the inverse system of Burgers equations is presented. Also, the convergence analysis and stability for this problem are investigated and the order of convergence is obtained. By using two test problems, the accuracy of presented method is verified. Additional...

In this paper, we propose a new interpolation technique using exponential B-spline, which is super-set of the Bspline. An interpolation kernel of exponential B-spline was proposed using IIR based technique by Unser. As another approach, this paper presents an exponential B-spline interpolation kernel using simple mathematics based on Fourier approximation. A high signal to noise ratio can be ac...

The non-local hyperbolic partial differential equations have many applications in sciences and engineering. A collocation finite element approach based on exponential cubic B-spline and quintic B-spline are presented for the numerical solution of the wave equation subject to nonlocal boundary condition. Von Neumann stability analysis is used to analyze the proposed methods. The efficiency, accu...

We give necessary and sufficient conditions for the total positivity of certain connection matrices arising in piecewise exponential spline spaces. These total positivity conditions are sufficient for existence of B-splines in such spaces, but they are far from being necessary. We give a necessary and sufficient condition for existence of B-splines in the case of piecewise exponential spline sp...

In this paper, the exponential B-spline functions are used for the numerical solution of the advection-diffusion equation. Two numerical examples related to pure advection in a finitely long channel and the distribution of an initial Gaussian pulse are employed to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies.

We construct a polynomial spline similar to the box spline, except that we relax the condition that its knots are spaced uniformly in each direction. The recurrence relation for this spline is a generalization of the recurrence relations for the box spline and univariate B-spline. The construction generalizes to exponential-polynomial splines [5]. §