[PDF] Top 20 A New Iterative Method for Riccati Differential Equation

... The Riccati differential equation is named after the Italian nobleman Count Jacopo Francesco Riccati ...of Riccati equation, with applications to random processes, optimal ... See full document

... fractional differential equations to the ordinary differential equations by using formulae (4) and (5), with the help of solving ordinary differential equations, the traveling wave solutions of ... See full document

... fractional-order Riccati differential equations will be ap- proached analytically by combining the Laplace transform, the Adomian decomposition method (ADM), and the Padé ...The method was extended by ... See full document

... long-wave equation and nonlinear dynamical system ...the new aspects of fractional calculus provide us with more stretchy mathematical models that help us to formulate more realistic judgments about ... See full document

... analytic method for nonlinear problems, namely HAM, [14, 15, ...perturbation method (HPM), which is a special case of HAM, to solve Riccati differential ...quadratic Riccati differen- ... See full document

... auxiliary equation method, many kinds of smooth type soliton, tense type soliton and peak soliton and so on new solutions of the nonlinear evolution equations have been obtained ...ordinary ... See full document

... Fokker-Planck equation into a system of ordinary differential equations suggested in( [15], [16]) ...collocation method to discretize space fractional diffusion equations to obtain a linear system of ... See full document

... recurrent differential equations which must be solved consecutively to give the approximate solution of the ...former method provides the solution of the problem without calculating Adomian’s ... See full document

... of new Preconditioned Modified Explicit Decoupled Group (PMEDG) for solving two dimensional steady Burgers' ...PMEDG iterative method is superior to the original MEDG method for solving the ... See full document

... the iterative process for finding the solutions of weakly nonlinear problem which is the modification of Newton method and converges with quadratic ... See full document

... of Riccati equation . In fact, the tangent vectors of differential equations have been computed for to get the same values exactly as given in [5], And show how Shortcut time for finding Lie Point ... See full document

... transformation method of Riccati equation has been successfully applied here for solving the Hamiltonian amplitude equation and the coupled Higgs field ...This method is an efficient ... See full document

... present method are compared with the modified homotopy perturbation method [22] by using fourth-order ...present method for this problem, we use estimated error kE(y N )k 2 in section ... See full document

... nonlinear equation. The new Simpson-type method is shown to converge of the order ...the new method requires the same amount of evaluations of the function and therefore the new ... See full document

... the method of averaging, the renormalization method, the method of multiple scales, the Lindstedt-Poincare method, the method of matched asymptotic expansions, plus their variants were ... See full document

... The Riccati equation plays a great role in blueprint and analysis the linear and nonlinear optimal control ...this equation has been acquired by applying Adomian’s decomposition method [1], ... See full document

... matrix equation in P, it is mostly preferred to use the Kleinman iteration by iteratively solving of LE (9) which is linear in P and then improving the controller by ...this method is the necessity of the ... See full document

... the Riccati equation, the general solution of the Riccati equation (1), cannot be easily ...numerical method, using hybrid of block-pulse functions, and Chebyshev polynomials for ... See full document

... The Riccati Matrix Differential Equation (RMDE) is an interesting equation in different fields of science and engineering ...matrix differential equation in the general case of ... See full document

... Now, an attention should be paid to Eq. (40). According to this result, we are led to conclude that one of the main advantages of the transformation given by Eq. (33) is that it converts Riccati equation ... See full document