Abstract
In this study, we consider the wave equation with cubic damping with its initial conditions. Homotopy Perturbation Method (HPM), Regular Pertubation Method (RPM) and Adomian decomposition Method (ADM) are applied to this equation. Then, the solution yielding the given initial conditions is gained. Finally, the solutions obtained by each method are compared.
Highlights
Over the last decades, several analytical/approximate methods have been developed to solve ordinary and partial differential equations
2.1 Basic Idea of the Homotopy Perturbation Method To illustrate the basic idea of HPM, consider the following nonlinear differential equation
The solution in equation (1) which obtained by HPM is absolutely same as that of the solution obtained by Adomian decomposition Method (ADM)
Summary
Several analytical/approximate methods have been developed to solve ordinary and partial differential equations. Some of these techniques include Homotopy Perturbation Method Approximate analytical solutions such as HPM, RPM and ADM were introduced, which are effective and convenient for both linear and nonlinear equations. Where ε is perturbation parameter which , u(t, x) is some physical quantity, x the space variable and t stands for time. These types of equations are of considerable significance in various fields of applied sciences, mathematical physics, nonlinear hydrodynamics, engineering physics, biophysics, human movement sciences, astrophysics and plasma physics.
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