scholarly journals On The Semi-Analytical Solution of Integro-Partial Differential Equations

2017 ◽  
Vol 139 ◽  
pp. 358-366
Author(s):  
Abdelmalek Hasseine ◽  
Menwer Attarakih ◽  
Rafik Belarbi ◽  
Hans Jörg Bart
Keyword(s):  
Partial Differential Equations ◽  
Analytical Solution ◽  
Differential Equations ◽  
Partial Differential

scholarly journals Analytical solution of Velocities and Temperature fields using Homotopy Analysis Method

2021 ◽  
Vol 12 (1S) ◽  
pp. 691-700
Author(s):  
Dr. K.V.Tamil Selvi , Et. al.
Keyword(s):  
Partial Differential Equations ◽  
Analytical Solution ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Nonlinear Differential Equations ◽  
Temperature Fields ◽  
Analysis Method ◽  
Partial Differential ◽  
Convective Boundary ◽  
Homotopy Analysis

In this paper, analysis of nonlinear partial differential equations on velocities and temperature with convective boundary conditions are investigated. The governing partial differential equations are transformed into ordinary differential equations by applying similarity transformations. The system of nonlinear differential equations are solved using Homotopy Analysis Method (HAM). An analytical solution is obtained for the values of Magnetic parameter M2, Prandtl number Pr, Porosity parameter

scholarly journals A Novel Homotopy Perturbation Algorithm Using Laplace Transform for Conformable Partial Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Sajad Iqbal ◽  
Mohammed K. A. Kaabar ◽  
Francisco Martínez
Keyword(s):  
Partial Differential Equations ◽  
Analytical Solution ◽  
Differential Equations ◽  
Laplace Transform ◽  
Homotopy Perturbation Method ◽  
Approximate Analytical Solution ◽  
Partial Differential ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions ◽  
Different Types

In this article, the approximate analytical solutions of four different types of conformable partial differential equations are investigated. First, the conformable Laplace transform homotopy perturbation method is reformulated. Then, the approximate analytical solution of four types of conformable partial differential equations is presented via the proposed technique. To check the accuracy of the proposed technique, the numerical and exact solutions are compared with each other. From this comparison, we conclude that the proposed technique is very efficient and easy to apply to various types of conformable partial differential equations.

scholarly journals Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 335 ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Muhammad Arif ◽  
Poom Kumam
Keyword(s):  
Partial Differential Equations ◽  
Analytical Solution ◽  
Differential Equations ◽  
Fractional Order ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Third Order ◽  
Partial Differential ◽  
Adomian Decomposition ◽  
In Series

In the present article, we related the analytical solution of the fractional-order dispersive partial differential equations, using the Laplace–Adomian decomposition method. The Caputo operator is used to define the derivative of fractional-order. Laplace–Adomian decomposition method solutions for both fractional and integer orders are obtained in series form, showing higher convergence of the proposed method. Illustrative examples are considered to confirm the validity of the present method. The fractional order solutions that are convergent to integer order solutions are also investigated.

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