In this paper, an approach based on statistical spline model (SSM) and collocation method is proposed to solve Volterra-Fredholm integral equations. The set of collocation nodes is chosen so that the points yield minimal error in the nodal polynomials. Under some standard assumptions, we establish the convergence property of this approach. Numerical results on some problems are given to describ...

A simple and explicit expression is given for the inner product of (higher order) derivatives of multivariate box splines and their translates. We also show that the energy inner product related to a linear partial differential equation discretized with a set of shifted box splines can be interpreted as a collocation of the problem with a higher order box spline at certain points.

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.  

In this paper, we present a mixed spline/spectral method to solve Volterra delay-integro-differential equations (VDIDEs). This method is based on generating the sextic spline collocation methods in all subintervals. The approximation of the integration in these subintervals, can be calculated by the El-Gendi method. Convergence results of the present method are presented. Numerical results are ...

In this paper, we develop a new cubic spline method for computing approximate solution of a system of fourth-order boundary value problems associated with obstacle, unilateral and contact problems. It is shown that the present method is of order two and gives approximations which are better than those produced by some other collocation, finite difference and spline methods. Numerical examples a...

In this work, we focus on a fractional differential equation in Riesz form discretized by polynomial B-spline collocation method. For an arbitrary degree p $$ , show that the resulting coefficient matrices possess Toeplitz-like structure. We investigate their spectral properties via symbol and prove that, like for second order problems, given are ill-conditioned both low high frequencies large ...

Among fitted-operator methods for solving one-dimensional singular perturbation problems one of the most accurate is the collocation by linear combinations of {1, x, exp (±px)}, known as tension spline collocation. There exist well established results for determining the ‘tension parameter’ p, as well as special collocation points, that provide higher order local and global convergence rates. H...