In this article, the problem of an incompressible viscous flow over a flat plate is presented. The homotopy perturbation method (HPM) is employed to solve the well-known Blasius nonlinear differential equation. It has been tried to use a new technique by which one be able to obtain solutions that are very close to the exact solution of the equation. The obtained results have been compared with ...

The main goal of this paper is to introduce a new scheme, known as the Aboodh homotopy integral transform method (AHITM), for approximate solution wave problems in multi-dimensional orders. (AIT) removes restriction variables recurrence relation, whereas perturbation (HPM) derives successive iterations using initial conditions. convergence analysis provided study equation with multiple dimensio...

In this article, we investigate the utilization of Riemann–Liouville’s fractional integral and Caputo derivative in application Optimal Auxiliary Function Method (OAFM). The extended OAFM is employed to analyze non-linear coupled ITO systems KDV systems, which feature equations a order time. We compare results obtained for system with those derived from Homotopy Perturbation (HPM) New Iterative...

In this paper we examine fluctuation and frequency of the governing equation ofoscillator with odd and even nonlinearities without damping and we present a new efficientmodification of the He’s homotopy perturbation method for this equation. We applied standard andmodified homotopy perturbation method and compare them with the numerical solution (NS), also weapplied He’s Energy balance method (...

Multispecies pollutant migration often occurs in polluted groundwater systems. Most of the multispecies problems that have been dealt literature assume constant transport parameters, primarily because analytical solutions for varying parameters become a challenge. The present study analytically solves two-species convection-dispersion equation, considering spatially dispersion coefficient and s...

although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.here, after criticizi...

Abstract The nonlinear two-dimensional forced-convection boundary-layer magneto hydrodynamic (MHD) incompressible flow of nanofluid over a horizontal stretching flat plate with variable magnetic field including the viscous dissipation effect is solved using the Variational iteration method (VIM), homotopy perturbation method (HPM) and Adomian decomposition method (ADM). In the paper, our result...