The Bezier Control Points Method for Solving Delay Differential Equation

Abstract

In this paper, Bezier surface form is used to find the approximate solution of delay differential equations (DDE’s). By using a recurrence relation and the traditional least square minimization method, the best control points of residual function can be found where those control points determine the approximate solution of DDE. Some examples are given to show efficiency of the proposed method

Approximate solution for quadratic Riccati differential equation

“…Zheng et al [13] proposed the use of control points of the Bernstein-Bezier form for solving differential equations numerically and also Evrenosoglu and Somali [14] used this approach for solving singular perturbed two points boundary value problems. Also the Bezier control points method is used for solving delay differential equation (see [15]). Some other applications of the Bezier functions and control points are found in (see [16]).…”

A Meshless Method For Solving Delay Differential Equation Using Radial Basis Functions With Error Analysis

“…The state and/or control involved in the equation are approximated by finite terms of orthogonal series and by using the operational matrix of integration the integral operations are eliminated. The form of the operational matrix of integration depends on the particular choice of the orthogonal functions like Walsh functions [4], Block-pulse functions [8], Laguerre series [9], Jacobi series [10], Fourier series [11], Bessel series [12], Taylor series [13], Shifted Legendre [14], Chebyshev polynomials [15] and Hermite polynomials [16]. In this study, we use wavelet functions to approximate both the control and state functions.…”

Bezier Curves Method for Fourth-Order Integrodifferential Equations

“…Hashim [4] determined the accuracy and efficiency of the ADM in solving integrodifferential equations. In the present work, we suggest a technique similar to the one which was used in [6][7][8] for solving both linear and nonlinear boundary value problems (BVPs) for fourth-order integrodifferential equations. Now, we consider the following class of two-point BVPs for fourth-order integrodifferential equations…”