A Study of General First-order Partial Differential Equations Using Homotopy Perturbation Method

Abstract

In this work, we have studied a general class of linear first-order partial differential equations which is used as mathematical models in many physically significant fields and applied science. The homotopy perturbation method (HPM) has been used for solving generalized linear first-order partial differential equation. Also, we have tested the HPM on the solving of different implementations which show the efficiency and accuracy of the method. The approximated solutions are agree well with analytical solutions for the tested problems Moreover, the approximated solutions proved that the proposed method to be efficient and high accurate.

Programming Variational Iteration Method via Wolfram-Mathematica for Solving Multi-Order Differential Equations

“…one part of this important equations is multi-order differential equations. Many researchers have studied this kind of differential equations by using different ways and methods, such as: generalized sine-cosine wavelets [13], Boubaker polynomials [1], homotopy analysis method [3], Legendre pseudo-spectral method [14], Chebyshev operational matrix method [4], and wavelet collocation method [5], Other related studies are on: modified HPM for solving generalized linear complex differential equations [9], solving fractional differential equations using Haar wavelet techniques [11], studies on the mathematical model of HIV infection of CD + 4 T by using HPM and VIM [2], studies of general second-order partial differential equations using HPM [6], of general first-order partial differential equations using HPM [7], and solving generalized Riccati differential equation [8]. One of the most popular methods for solving equations is variational iteration (VIM), and in the present work we use this method for solving a class of multi-order ordinary differential equation.…”