[PDF] Top 20 Variational Homotopy Perturbation Method for Solving Riccati Type Differential Problems

... The Riccati equation plays a great role in blueprint and analysis the linear and nonlinear optimal control ...decomposition method [1], homotopy Analysis method HAM [2], variational ... See full document

... engineering problems, there is a growing interest in exploring new methods to solve the equation more accurately and efficiently ...partial differential equations by using various ...decomposition ... See full document

... This method is based on the use of traditional perturbation method and homotopy ...this method, the solution is considered as the summation of an infinite series which converges rapidly ... See full document

... [14] Homotopy perturbation method applied to solve variational problems with fixed ...of variational problems with moving boundaries problems can be obtained by ... See full document

... efficient method for solving the quadratic Riccati differential ...new homotopy perturbation methods (LTNHPM) are considered as an algorithm to the exact solution of the ... See full document

... governing differential equations do not have analytical solutions in genuine events in nature and ...the homotopy perturbation method (HPM) [1-23], variational iteration method ... See full document

... the homotopy perturbation method (HPM) [1, 7] in nonlinear problems has been developed by scientists and engineers, because this method continuously deforms the difficult problem under ... See full document

... , 0, ∈ Γ (6) Where is a general differential operator. is a known analytic function, Γ is the boundary of the domain Ω and denotes directionalderivative in outward normal direction to Ω. The operator , ... See full document

... Perturbation Method (LHPM) was utilized to solve some nonlinear partial differential ...transform method and the homotopy perturbation ...partial differential ... See full document

... Integral-differential equations appear in many scientific applications, especially when we convert initial value problems or boundary value problems to integral equations. The ... See full document

... transfer problems which are known to arise in a variety of physical phenomenon and applied sciences [1, ...the variational iteration and homotopy perturbation methods for solving ... See full document

... He’s Homotopy perturbation method of solving linear and non-linear Fredholm Integro-Differential Equation and conducted a comparative study between He’s Homotopy ... See full document

... nonlinear differential equations of fractional order, which became requires researchers to use conventional methods to solve ...the homotopy perturbation method (HPM). This method was ... See full document

... the variational iteration method and the homotopy perturbation method to solve Sturm-Liouville eigenvalue and boundary value ...nonlinear problems without linearization or ... See full document

... the homotopy in topology to propose a general analytic method for nonlinear problems, namely HAM, [14, 15, ...applied homotopy perturbation method (HPM), which is a special case ... See full document

... the Riccati equation in an explicit form seems an unlikely concept except for certain special situations as discussed above, however, that can easily be overcome if its one particular solution is ...Decomposition ... See full document

... -expansion method [4] and Hirota bilinear method ...decomposition method (ADM) [7], He’s Semi- inverse method [8], the tanh method, homotopy perturba- tion method(HPM), ... See full document

... this method, the time interval is divided into n equal subintervals and the method is applied once to each ...the Riccati equation by the homo- topy perturbation method [1], the ... See full document

... the variational iteration method using He’s polynomials for finding the analytical solution of gas dynamic ...proposed method is an elegant combination of He’s variational iteration and the ... See full document

... (9) where p and ρ are pressure and density, respectively. For solving equations (7)-(9), we must apply boundary conditions (equations (5) and (6)). Other boundary conditions are no lateral velocity and pressure ... See full document