Numerical Solution and Error Analysis for Linear and Nonlinear Delay Differential Equations

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AMINI EBRAHIM; Ebadian Ali

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ISSN: 2588-4824

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2020 | Volume:6 | Issue:25 Page(s): 83-98

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Title

Numerical Solution and Error Analysis for Linear and Nonlinear Delay Differential Equations

Author(s)

AMINI EBRAHIM | Ebadian Ali | Issue Writer Certificate

Keywords

Reproducing kernel

Delay differential equations

Error analysis

Convergence analysis

Abstract

In this paper, we obtain the solution of linear and nonlinear Delay differential equations in Reproducing kernel space. For this purpose, regarding the equation and conditions governing it, a linear operator is defined and subsequently an orthonormal complete system for Reproducing kernel space is obtained by using the adjoint operator and Reproducing kernel function. Then, the solution of these equations is obtained in the form of a series of the basic functions. Indeed, the analytical solution is represented by infinite series, and the approximate solution is obtained by using an iterative method. As one of the main aims, the Convergence analysis and error behavior are discussed for the proposed method. Finally, some numerical examples are studied to demonstrate the validity and applicability of the proposed method. The obtained results of the proposed method are compared with the exact solutions and the earlier works. The outcomes from numerical examples illustrate that the proposed method is very effective and convenient.

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APA: Copy

AMINI, EBRAHIM, & Ebadian, Ali. (2020). Numerical Solution and Error Analysis for Linear and Nonlinear Delay Differential Equations. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 6(25 ), 83-98. SID. https://sid.ir/paper/977144/en

Vancouver: Copy

AMINI EBRAHIM, Ebadian Ali. Numerical Solution and Error Analysis for Linear and Nonlinear Delay Differential Equations. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2020;6(25 ):83-98. Available from: https://sid.ir/paper/977144/en

IEEE: Copy

EBRAHIM AMINI, and Ali Ebadian, “Numerical Solution and Error Analysis for Linear and Nonlinear Delay Differential Equations,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 6, no. 25 , pp. 83–98, 2020, [Online]. Available: https://sid.ir/paper/977144/en

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