scholarly journals Analytical Aspect of Fourth-Order Parabolic Partial Differential Equations with Variable Coefficients

2010 ◽  
Vol 15 (3) ◽  
pp. 481-489 ◽  
Author(s):  
Najeeb Khan ◽  
Asmat Ara ◽  
Muhammad Afzal ◽  
Azam Khan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fourth Order ◽  
Variable Coefficients ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Analytical Aspect

The Solution of the Variable Coefficients Fourth-Order Parabolic Partial Differential Equations by the Homotopy Perturbation Method

2009 ◽  
Vol 64 (7-8) ◽  
pp. 420-430 ◽  
Author(s):  
Mehdi Dehghan ◽  
Jalil Manafian
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Fourth Order ◽  
Homotopy Perturbation Method ◽  
Variable Coefficients ◽  
Parabolic Partial Differential Equation ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Homotopy Perturbation

AbstractIn this work, the homotopy perturbation method proposed by Ji-Huan He [1] is applied to solve both linear and nonlinear boundary value problems for fourth-order partial differential equations. The numerical results obtained with minimum amount of computation are compared with the exact solution to show the efficiency of the method. The results show that the homotopy perturbation method is of high accuracy and efficient for solving the fourth-order parabolic partial differential equation with variable coefficients. The results show also that the introduced method is a powerful tool for solving the fourth-order parabolic partial differential equations.

scholarly journals Three-Dimensional Fourth-Order Time-Fractional Parabolic Partial Differential Equations and Their Analytical Solution

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yesuf Obsie Mussa ◽  
Ademe Kebede Gizaw ◽  
Ayana Deressa Negassa
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fourth Order ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Variable Coefficients ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Differential Transform

In this study, the fractional reduced differential transform method (FRDTM) is employed to solve three-dimensional fourth-order time-fractional parabolic partial differential equations with variable coefficients. The fractional derivative used in this study is in the Caputo sense. A few important lemmas which are essential to solve the problems using the proposed method are proved. The novelty of this method is that it uses appropriate initial conditions and finds the solution to the problems without any discretization, linearization, perturbation, or any restrictive assumptions. Two numerical examples are considered in order to validate the efficiency and reliability of the method. Furthermore, the FRDTM solution when α = 1 is compared with other analytical methods available in the existing literature. Computational results are shown in tables and graphs. The obtained results revealed that the method is capable and simple to solve fractional partial differential equations. The software used for the calculations in this study is Mathematica 7.

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