This paper presents the study of a numerical scheme for analytical solution nonlinear gas dynamic equation. We use idea Laplace–Carson transform and associate it with homotopy perturbation method (HPM) obtaining series show that this hybrid approach is excellent in agreement converges to exact very smoothly. Further, HPM combined He’s polynomial utilized minimize simulations conditions make eas...

In this research, we propose a combined approach to solving nonlinear fractional shock wave equations using an Elzaki transform, the homotopy perturbation method, and Adomian decomposition method. The equation is first transformed into equivalent integral transform. method are then utilized approximate solution of equation. To evaluate effectiveness proposed conduct several numerical experiment...

In this study, we present a new general solution to rational epidemiological mathematical model via recent intelligent method called the natural transform homotopy analysis (NTHAM), which combines two methods: (NTM) and (HAM). To assess precision reliability of method, compared obtained results with those Laplace perturbation (LHPM) as well q-homotopy Sumudu (q-HASTM), revealed that NTHAM is mo...

In this paper, we tried to accelerate the rate of convergence in solving second-order Fredholm type Integro-differential equations using a new method which is based on Improved homotopy perturbation method (IHPM) and applying accelerating parameters. This method is very simple and the result is obtained very fast.  

In this paper, the Sawada-Kotera equation is solved by using the Adomian’s decomposition method, modified Adomian’s decomposition method, variational iteration method, modified variational iteration method, homotopy perturbation method, modified homotopy perturbation method and homotopy analysis method. The approximate solution of this equation is calculated in the form of series which its comp...

This article is an analysis of fractional nonlinear convection–reaction–diffusion equations involving the Atangana–Baleanu and Caputo derivatives. An efficient Aboodh homotopy perturbation transform method, which combines method with transformation, applied to investigate this fractional-order proposed model, analytically. A modified technique known as formulated approximate these The analytica...

This paper presents an approximate analytical solution of the nonlinear Fornberg-Whitham equation using the new iterative method (NIM). A comparison is made between the NIM results, homotopy perturbation transform method (HPTM) and the Adomian's decomposition method (ADM). The solution procedure reveals that NIM is a reliable, simple and effective. The proposed technique solves nonlinear proble...