A modified homotopy perturbation method for singular time dependent Emden–Fowler equations with boundary conditions

2016 ◽  
Vol 54 (4) ◽  
pp. 918-931 ◽  
Author(s):  
Randhir Singh ◽  
Sukhjit Singh ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Boundary Conditions ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Time Dependent ◽  
Homotopy Perturbation ◽  
Singular Time

THE FRACTIONAL COMPLEX TRANSFORM: A NOVEL APPROACH TO THE TIME-FRACTIONAL SCHRÖDINGER EQUATION

Fractals ◽  
2020 ◽  
Vol 28 (07) ◽  
pp. 2050141
Author(s):  
QURA TUL AIN ◽  
JI-HUAN HE ◽  
NAVEED ANJUM ◽  
MUHAMMAD ALI
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Time Dependent ◽  
Nonlinear Part ◽  
Fractional Complex Transform ◽  
Homotopy Perturbation ◽  
Novel Approach ◽  
Time Fractional Derivative

This paper presents a thorough study of a time-dependent nonlinear Schrödinger (NLS) differential equation with a time-fractional derivative. The fractional time complex transform is used to convert the problem into its differential partner, and its nonlinear part is then discretized using He’s polynomials so that the homotopy perturbation method (HPM) can be applied powerfully. The two-scale concept is used to explain the substantial meaning of the fractional time complex transform and the solution.

scholarly journals Homotopy Perturbation Method for Solving Wave-Like Nonlinear Equations with Initial-Boundary Conditions

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Afgan Aslanov
Keyword(s):  
Boundary Conditions ◽  
Perturbation Method ◽  
Nonlinear Equations ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Initial Boundary ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions

The homotopy perturbation method is employed to obtain approximate analytical solutions of the wave-like nonlinear equations with initial-boundary conditions. An efficient way of choosing the auxiliary operator is presented. The results demonstrate reliability and efficiency of the method.

scholarly journals Analytical exact solution of telegraph equation using HPM

BIBECHANA ◽  
2016 ◽  
Vol 14 ◽  
pp. 30-36
Author(s):  
Jamshad Ahmad ◽  
Ghulam Mohiuddin
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Boundary Conditions ◽  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Iterative Scheme ◽  
Nonlinear Partial Differential Equations ◽  
Telegraph Equation ◽  
Homotopy Perturbation

In this paper, exact solutions of different variants of second order hyperbolic telegraph equation are investigated with Homotopy Perturbation Method (HPM). The results determined by the proposed method are quite satisfactory and shows that HPM technique is very effective and useful for solving the nonlinear partial differential equations (PDEs) with given initial or boundary conditions. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions.BIBECHANA 14 (2017) 30-36

scholarly journals New reliable modifications of HPM and HAM

2020 ◽  
Vol 19 (1) ◽  
pp. 371
Author(s):  
Khawlah Hussain
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Comparative Study ◽  
Perturbation Method ◽  
Homotopy Analysis Method ◽  
Homotopy Perturbation Method ◽  
Analysis Method ◽  
Homotopy Perturbation ◽  
Homotopy Analysis

<p>In this article, a new modification of the homotopy perturbation method (HPM) and homotopy analysis method (HAM) is presented and applied to non-homogeneous fractional Volterra integro-differential equations with boundary conditions. A comparative study between the new modified homotopy perturbation method (MHPM) and the new modified homotopy analysis method (MHAM). Several illustrative examples are given to demonstrate the effectiveness and reliability of the methods.</p>

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