Methods For Approximating And Stabilizing The Solution Of Nonlinear Riccati Matrix Delay Differential Equation - Mohammedali, Khalid Hammood (2019)
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.