New iterative method for solving gas dynamic equation

Abstract

In this paper, the gas dynamic equation is solved through new iterative method (NIM). The obtained results are compared with those of homotopy perturbation method (HPM), variational iteration method with He's polynomials (VIMHP) and Laplace transform new homotopy perturbation method (LTNHPM). It is noted that the NIM in case of nonhomogeneous problems takes the form of a convergent series with easily computable components. This method is able to solve large class of linear and nonlinear equations effectively, more easily and accurately; and thus the method has been widely applicable to solve any class of equations in sciences and engineering.

An analytical treatment to fractional Fornberg–Whitham equation

“…To describe the idea of the NIM, consider the following general functional equation [10,[16][17][18][19][20]:…”

New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations

“…To describe the idea of the NIM, consider the following general functional equation [ 19 – 22 ]: where N is a nonlinear operator from a Banach space B → B and f is a known function. We are looking for a solution u of ( 6 ) having the series form The nonlinear operator N can be decomposed as follows: From ( 7 ) and ( 8 ), ( 6 ) is equivalent to We define the recurrence relation: Then If N is a contraction, that is, then and the series ∑ i =0 ∞ u i absolutely and uniformly converges to a solution of ( 6 ) [ 23 ], which is unique, in view of the Banach fixed point theorem [ 24 ].…”

The best parameters selection using pso algorithm to solving for ito system by new iterative technique

“…The main aim of using the new iterative method proposed by Jafari and Daftardar [9][10][11], and has been modifed by Hameda [12][13][14], to resolve the partial and ordinary linear and nonlinear differential equations, and give the importance of equations and their applications in various practical fields and this is the basis on which the application of this method [15][16][17][18][19][20]. The new iterative method NIM technique is unpretentious to grasp and easy to do on the computer and has very effective results, which gave it a great benefit in resolving a variety of equations including algebraic and integral and partial and normal differential equations with the correct and fractional ranks and systems of equations [21].…”