Methods For Approximating And Stabilizing The Solution Of Nonlinear Riccati Matrix Delay Differential Equation

where ,A B and C are nn matrices such that , TBB TCC and ( ) . nn X t R   This nonlinear Riccati matrix differential equation may also be viewed as a quadratic ordinary differential equation. The above equation may be generalized for delay differential equations with retarded arguments, in w...

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Main Author:	Mohammedali, Khalid Hammood
Format:	Thesis
Language:	English
Published:	2019
Subjects:	QA1 Mathematics (General)
Online Access:	http://eprints.usm.my/48573/1/KHALID%20HAMMOOD%20MOHAMMEDALI%20cut.pdf
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spelling	my-usm-ep.485732021-03-09T09:03:39Z Methods For Approximating And Stabilizing The Solution Of Nonlinear Riccati Matrix Delay Differential Equation 2019-03 Mohammedali, Khalid Hammood QA1 Mathematics (General) where ,A B and C are nn matrices such that , TBB TCC and ( ) . nn X t R   This nonlinear Riccati matrix differential equation may also be viewed as a quadratic ordinary differential equation. The above equation may be generalized for delay differential equations with retarded arguments, in which the delay term occurs as a constant time delay in ()Xt but not in ()Xt (the derivative will disappear and the equation will become algebraic Riccati matrix equation after the initial condition is used). In this thesis we study the variational iteration method and use it to solve nonlinear Riccati matrix differential equation and nonlinear Riccati matrix delay differential equations. The solution approach requires, initially, the derivation of the variational iteration method for solving such types of equations and then proof of its convergence to the exact solution in two cases with and without delay. The Adomian decomposition method is then applied for solving nonlinear Riccati matrix differential equation in two cases with and without delay. 2019-03 Thesis http://eprints.usm.my/48573/ http://eprints.usm.my/48573/1/KHALID%20HAMMOOD%20MOHAMMEDALI%20cut.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Sains Matematik
institution	Universiti Sains Malaysia
collection	USM Institutional Repository
language	English
topic	QA1 Mathematics (General)
spellingShingle	QA1 Mathematics (General) Mohammedali, Khalid Hammood Methods For Approximating And Stabilizing The Solution Of Nonlinear Riccati Matrix Delay Differential Equation
description	where ,A B and C are nn matrices such that , TBB TCC and ( ) . nn X t R   This nonlinear Riccati matrix differential equation may also be viewed as a quadratic ordinary differential equation. The above equation may be generalized for delay differential equations with retarded arguments, in which the delay term occurs as a constant time delay in ()Xt but not in ()Xt (the derivative will disappear and the equation will become algebraic Riccati matrix equation after the initial condition is used). In this thesis we study the variational iteration method and use it to solve nonlinear Riccati matrix differential equation and nonlinear Riccati matrix delay differential equations. The solution approach requires, initially, the derivation of the variational iteration method for solving such types of equations and then proof of its convergence to the exact solution in two cases with and without delay. The Adomian decomposition method is then applied for solving nonlinear Riccati matrix differential equation in two cases with and without delay.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Mohammedali, Khalid Hammood
author_facet	Mohammedali, Khalid Hammood
author_sort	Mohammedali, Khalid Hammood
title	Methods For Approximating And Stabilizing The Solution Of Nonlinear Riccati Matrix Delay Differential Equation
title_short	Methods For Approximating And Stabilizing The Solution Of Nonlinear Riccati Matrix Delay Differential Equation
title_full	Methods For Approximating And Stabilizing The Solution Of Nonlinear Riccati Matrix Delay Differential Equation
title_fullStr	Methods For Approximating And Stabilizing The Solution Of Nonlinear Riccati Matrix Delay Differential Equation
title_full_unstemmed	Methods For Approximating And Stabilizing The Solution Of Nonlinear Riccati Matrix Delay Differential Equation
title_sort	methods for approximating and stabilizing the solution of nonlinear riccati matrix delay differential equation
granting_institution	Universiti Sains Malaysia
granting_department	Pusat Pengajian Sains Matematik
publishDate	2019
url	http://eprints.usm.my/48573/1/KHALID%20HAMMOOD%20MOHAMMEDALI%20cut.pdf
_version_	1747821949661216768

Methods For Approximating And Stabilizing The Solution Of Nonlinear Riccati Matrix Delay Differential Equation

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