The derivation of convergence analysis for the multistage adomian decomposition method for solving the autonomous van der pol system
Joint Authors
al-Bayati, Abbas Y.
al-Sawur, Ann J.
Samarji, Merna A.
Source
al-Tarbiyah wa-al-Ilm : Majallat ilmiyah lil-Buhuth al-Ilmiyah al-Asasiyah
Issue
Vol. 24, Issue 3 (30 Sep. 2011), pp.133-148, 16 p.
Publisher
University of Mosul College of Education for Pure Science
Publication Date
2011-09-30
Country of Publication
Iraq
No. of Pages
16
Main Subjects
Abstract EN
The autonomous Van der Pol system was solved accurately by MADM [4].
The method has the advantage of giving the form of the numerical solution within each time interval which is not possible in purely numerical techniques like RK45 and classical ADM.
In this paper we will derive the convergence of A Multistage Adomian Decomposition Method (MADM) by deriving the Homotopy Analysis Method for this system.
We will show that if the series 2 1 0 0 1 ( 0) ( ) j n t n i ij in in x t a x dt x t dt where 2 1 0 0 i2 2 1 0 0 , 1 ) , , ( R ~ ! 1 ! ~ ( , ) ! ~ ( ) ( ) p t n p q n q ipq n i n i in dt n d d x x n a n d d x t n x t x t is convergent and it must be a solution of Van der Pol system, then the two sequences ( ) , ( ) 1 1 R t v h t k n k in k n k in are converges to zero.
American Psychological Association (APA)
al-Bayati, Abbas Y.& al-Sawur, Ann J.& Samarji, Merna A.. 2011. The derivation of convergence analysis for the multistage adomian decomposition method for solving the autonomous van der pol system. al-Tarbiyah wa-al-Ilm : Majallat ilmiyah lil-Buhuth al-Ilmiyah al-Asasiyah،Vol. 24, no. 3, pp.133-148.
https://search.emarefa.net/detail/BIM-621786
Modern Language Association (MLA)
al-Bayati, Abbas Y.…[et al.]. The derivation of convergence analysis for the multistage adomian decomposition method for solving the autonomous van der pol system. al-Tarbiyah wa-al-Ilm : Majallat ilmiyah lil-Buhuth al-Ilmiyah al-Asasiyah Vol. 24, no. 3 (2011), pp.133-148.
https://search.emarefa.net/detail/BIM-621786
American Medical Association (AMA)
al-Bayati, Abbas Y.& al-Sawur, Ann J.& Samarji, Merna A.. The derivation of convergence analysis for the multistage adomian decomposition method for solving the autonomous van der pol system. al-Tarbiyah wa-al-Ilm : Majallat ilmiyah lil-Buhuth al-Ilmiyah al-Asasiyah. 2011. Vol. 24, no. 3, pp.133-148.
https://search.emarefa.net/detail/BIM-621786
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 147-148
Record ID
BIM-621786