the spline collocation method  is employed to solve a system of linear and nonlinear fredholm and volterra integro-differential equations. the solutions are collocated by cubic b-spline and the integrand is approximated by the newton-cotes formula. we obtain the unique solution for linear and nonlinear system $(nn+3n)times(nn+3n)$ of integro-differential equations. this approximation reduces th...

Published 1. End Conditions for Interpolatory Septic Spline Ghazala Akram and Shahid S. Siddiqi, International Journal of Computer Mathematics, Vol. 82, No. 12, 2005 pp15251540. 2. Solutions of Fifth Order Boundary-Value Problems Using NonPolynomial Spline Technique Shahid S. Siddiqi and Ghazala Akram, Applied Mathematics and Computation Vol. 175, No. 2, 2006 pp. 1574-1581. 3. Solutions of Sixt...

In this paper, Semi-orthogonal (SO) B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of linear and non-linear second order Fredholm integro-differential equations. The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this functions are presented to reduce the solution of linear and...

Abstract: The aim of study is to solve parabolic integro-differential equation with a weakly singular kernel. Problems involving partial integro-differential equations arise in fluid dynamics, viscoelasticity, engineering, mathematical biology, financial mathematics and other areas. Many mathematical formulations of physical phenomena contain integro-differential equations. Integro-differential...

In this paper simple quartic trigonometric polynomial blending functions, with a tensionparameter, are presented. These type of functions are useful for constructing trigonometricB´ezier curves and surfaces, they can be applied to construct continuous shape preservinginterpolation spline curves with shape parameters. To better visualize objects and graphics atension parameter is included. In th...

In this work, we study quasi-interpolation in a space of sextic splines defined over Powell–Sabin triangulations. These spline functions are class C2 on the whole domain but fourth-order regularity is required at vertices and C3 imposed across edges refined triangulation also interior point chosen to define refinement. An algorithm proposed triangles with small area diameter needed construct no...

A computationally inexpensive algorithm for signal interpolation using B-spline functions is presented in this work. Speciically, the convolution between the B-spline coeecients and the B-spline function itself, widely acknowledged as the most costly aspect of B-spline interpolation, is reformulated such that it is directly amenable to implementation at a much lower computational cost (16.25% o...