A family of fourth and second-order accurate numerical schemes is presented for the solution of nonlinear fourth-order boundary-value problems (BVPs) with two-point boundary conditions. Non-polynomial quintic spline functions are applied to construct the numerical algorithms. This approach generalizes nonpolynomial spline algorithms and provides a solution at every point of the range of integra...

In this paper, we provide an interpretation of polynomial spline interpolation as a continuous filtering process. We prove that the frequency responses of the cardinal spline filters converge to the ideal lowpass filter in all L f n o r m s with 1 ~<p < + ~ as the order of the spline tends to infinity. We provide estimates for the resolution errors and the interpolation errors of the various fi...

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...

The multi-frontal direct solver is the state-of-the-art algorithm for the direct solution of sparse linear systems. This paper provides computational complexity and memory usage estimates for the application of the multifrontal direct solver algorithm on linear systems resulting from B-spline-based isogeometric finite elements, where the mesh is a structured grid. Specifically we provide the es...

The problem of semi-cardinal spline interpolation was solved by Schoenberg exploiting the piecewise polynomial form of the splines. In the present paper, we propose a new construction for the Lagrange functions of semi-cardinal spline interpolation , based on a radial basis and Fourier transform approach. This approach suggests a way of extending semi-cardinal interpolation to polyharmonic spli...

Second and fourth order convergent methods based on Quartic nonpolynomial spline function are presented for the numerical solution of a third order two-point boundary value problem. The proposed approach gives better approximations than existing polynomial spline and finite difference methods and has a lower computational cost. Convergence analysis of the proposed method is discussed; two numer...

Spline curves are very prominent in the mathematics due to their simple construction, accuracy of assessment and ability approximate complicated structures into interactive curved designs. A spline is a smooth piece-wise polynomial function. The primary goal this study use extended cubic B-spline (ExCuBS) functions with new second order derivative approximation obtain numerical solution weakly ...

Multi-degree Tchebycheffian splines are with pieces drawn from extended (complete) Tchebycheff spaces, which may differ interval to interval, and possibly of different dimensions. These a natural extension multi-degree polynomial splines. Under quite mild assumptions, they can be represented in terms so-called B-spline (MDTB-spline) basis; such basis possesses all the characterizing properties ...