# A new approach for numerical solution of a linear system with distributed delays, Volterra delay-integro-differential equations, and nonlinear Volterra-Fredholm integral equation by Bezier curves

A new approach for numerical solution of a linear system with distributed delays, Volterra... In this paper, we present Bezier curves method to solve Volterra delay-integro-differential equations. Also, this paper is concerned with a linear system with distributed input delay and input saturation. The approximation process by Bezier curves method is done in two steps. First we divide the time interval into 2k subintervals, second approximate the trajectory and control functions in each subinterval by Bezier curves. We have chosen the Bezier curves as piecewise polynomials of degree n, and determine Bezier curves on any subinterval by \$\$n+1\$\$ n + 1 control points. Also, we have used Bezier curves method to solve linear and nonlinear Volterra-Fredholm integral equations, numerically. The proposed method is simple and computationally advantageous. Some numerical examples demonstrate the validity and applicability of the technique. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational and Applied Mathematics Springer Journals

# A new approach for numerical solution of a linear system with distributed delays, Volterra delay-integro-differential equations, and nonlinear Volterra-Fredholm integral equation by Bezier curves

, Volume 36 (3) – Nov 20, 2015
17 pages

/lp/springer_journal/a-new-approach-for-numerical-solution-of-a-linear-system-with-UVkPz0gNB7
Publisher
Springer International Publishing
Subject
Mathematics; Applications of Mathematics; Computational Mathematics and Numerical Analysis; Mathematical Applications in the Physical Sciences; Mathematical Applications in Computer Science
ISSN
0101-8205
eISSN
1807-0302
D.O.I.
10.1007/s40314-015-0296-2
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we present Bezier curves method to solve Volterra delay-integro-differential equations. Also, this paper is concerned with a linear system with distributed input delay and input saturation. The approximation process by Bezier curves method is done in two steps. First we divide the time interval into 2k subintervals, second approximate the trajectory and control functions in each subinterval by Bezier curves. We have chosen the Bezier curves as piecewise polynomials of degree n, and determine Bezier curves on any subinterval by \$\$n+1\$\$ n + 1 control points. Also, we have used Bezier curves method to solve linear and nonlinear Volterra-Fredholm integral equations, numerically. The proposed method is simple and computationally advantageous. Some numerical examples demonstrate the validity and applicability of the technique.

### Journal

Computational and Applied MathematicsSpringer Journals

Published: Nov 20, 2015

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