Abstract
An efficient modification and a novel technique combining the homotopy concept with Adomian decomposition method (ADM) to obtain an accurate analytical solution for Riccati matrix delay differential equation (RMDDE) is introduced in this paper . Both methods are very efficient and effective. The whole integral part of ADM is used instead of the integral part of homotopy technique. The major feature in current technique gives us a large convergence region of iterative approximate solutions .The results acquired by this technique give better approximations for a larger region as well as previously. Finally, the results conducted via suggesting an efficient and easy technique, and may be addressed to other non-linear problems.
Highlights
IntroductionLiao implemented the initial thoughts of homotopy in topology to suggest a semi analytic approach for non-linear equations, called Homotopy Analysis Method (HAM); 1, 2
In this study, a homotopy –Adomian approach is presented for addressing the following Riccati matrix delay differential equation (RMDDE): G(t) Z0 (t), c t c, c is non negative integer number.For many years, Liao implemented the initial thoughts of homotopy in topology to suggest a semi analytic approach for non-linear equations, called Homotopy Analysis Method (HAM); 1, 2.According to homotopy of topology, the evidence of this approach exists with or without small physical parameters in the considered problem
It is an analytic approach for finding series solution of various kinds of non-linear problems 3
Summary
Liao implemented the initial thoughts of homotopy in topology to suggest a semi analytic approach for non-linear equations, called Homotopy Analysis Method (HAM); 1, 2. According to homotopy of topology, the evidence of this approach exists with or without small physical parameters in the considered problem It is an analytic approach for finding series solution of various kinds of non-linear problems 3. ADM since 1980s, is an example of a semi analytic approach which can be implemented to many kinds of equations including non-linear PDEs 5, 6, 7 It gives an effective computational manner for equations and can get results as an infinite series converging to exact solution 6, 8, 9. The most important advantages of these methods is its ability in providing us a continuous representation of the approximate solution, which allows better information of the results with whole interval In addition it gives a highly accurate solution. G(t) Z0(t), Consider with the method of successive for delay, generally for every time step [c i ,c (i 1) ], i 0,1,..., N; N R
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