کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
767008 | 897140 | 2012 | 16 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Numerical solution of the delay differential equations of pantograph type via Chebyshev polynomials Numerical solution of the delay differential equations of pantograph type via Chebyshev polynomials](/preview/png/767008.png)
In this article we propose a numerical scheme to solve the pantograph equation. The method consists of expanding the required approximate solution as the elements of the shifted Chebyshev polynomials. The Chebyshev pantograph operational matrix is introduced. The operational matrices of pantograph, derivative and product are utilized to reduce the problem to a set of algebraic equations. An error analysis is presented which allows the number of polynomials employed in the approximation to be selected in advance for a desired tolerance. Some examples are given to demonstrate the validity and applicability of the new method and a comparison is made with the existing results.
► In the current paper a numerical technique is proposed.
► Numerical approximation is based on shifted Chebyshev polynomials.
► The operational matrices of derivative and product are utilized.
► The new technique is used to solve several test examples.
► Model is a delay differential equation which has many applications.
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 17, Issue 12, December 2012, Pages 4815–4830