scholarly journals A new technology for solving diffusion and heat equations

2017 ◽  
Vol 21 (1 Part A) ◽  
pp. 133-140 ◽  
Author(s):  
Xiao-Jun Yang ◽  
Feng Gao
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Iterative Method ◽  
Integral Transform ◽  
New Technology ◽  
Approximate Solutions ◽  
Heat Equations ◽  
Sumudu Transform ◽  
First Time ◽  
Variational Iterative Method

In this paper, a new technology combing the variational iterative method and an integral transform similar to Sumudu transform is proposed for the first time for solutions of diffusion and heat equations. The method is accurate and efficient in development of approximate solutions for the partial differential equations.

scholarly journals Application of Sumudu Decomposition Method to Solve Nonlinear System of Partial Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Hassan Eltayeb ◽  
Adem Kılıçman
Keyword(s):  
Partial Differential Equations ◽  
Nonlinear System ◽  
Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Partial Differential ◽  
Adomian Polynomials ◽  
Adomian Decomposition ◽  
Sumudu Transform

We develop a method to obtain approximate solutions of nonlinear system of partial differential equations with the help of Sumudu decomposition method (SDM). The technique is based on the application of Sumudu transform to nonlinear coupled partial differential equations. The nonlinear term can easily be handled with the help of Adomian polynomials. We illustrate this technique with the help of three examples, and results of the present technique have close agreement with approximate solutions obtained with the help of Adomian decomposition method (ADM).

scholarly journals A New Approach on Transforms: Formable Integral Transform and Its Applications

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 332
Author(s):  
Rania Zohair Saadeh ◽  
Bayan fu’ad Ghazal
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Integral Transform ◽  
Sufficient Conditions ◽  
Partial Differential ◽  
New Approach ◽  
Essential Properties ◽  
The Laplace Transform ◽  
Sumudu Transform ◽  
Definition Of

In this paper, we introduce a new integral transform called the Formable integral transform, which is a new efficient technique for solving ordinary and partial differential equations. We introduce the definition of the new transform and give the sufficient conditions for its existence. Some essential properties and examples are introduced to show the efficiency and applicability of the new transform, and we prove the duality between the new transform and other transforms such as the Laplace transform, Sumudu transform, Elzaki transform, ARA transform, Natural transform and Shehu transform. Finally, we use the Formable transform to solve some ordinary and partial differential equations by presenting five applications, and we evaluate the Formable transform for some functions and present them in a table. A comparison between the new transform and some well-known transforms is made and illustrated in a table.

scholarly journals Some Applications of The New Integral Transform For Partial Differential Equations

2018 ◽  
Vol 7 (1) ◽  
pp. 45-49
Author(s):  
S L Shaikh
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Integral Transform ◽  
Partial Differential ◽  
Partial Derivatives ◽  
The Laplace Transform ◽  
Sumudu Transform ◽  
Function Of Two Variables ◽  
Derivatives Of

In this paper we have derived Sadik transform of the partial derivatives of a function of two variables. We have demonstrated the applicability of the Sadik transform by solving some examples of partial differential equations. We have verified solutions of partial differential equations by Sadik transform with the Laplace transform and the Sumudu transform.

scholarly journals Applications of New Double Integral Transform (Laplace–Sumudu Transform) in Mathematical Physics

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Shams A. Ahmed
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Integral Transform ◽  
Mathematical Physics ◽  
High Accuracy ◽  
Double Integral ◽  
Partial Differential ◽  
Fundamental Properties ◽  
Sumudu Transform ◽  
Basic Functions

The primary purpose of this research is to demonstrate an efficient replacement of double transform called the double Laplace–Sumudu transform (DLST) and prove some related theorems of the new double transform. Also, we will discuss the fundamental properties of the double Laplace–Sumudu transform of some basic functions. Then, by utilizing those outcomes, we will apply it to the partial differential equations to show its simplicity, efficiency, and high accuracy.

scholarly journals Exact Solution of Two-Dimensional Fractional Partial Differential Equations

2020 ◽  
Vol 4 (2) ◽  
pp. 21 ◽  
Author(s):  
Dumitru Baleanu ◽  
Hassan Kamil Jassim
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Approximate Solutions ◽  
Two Dimensional ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Sumudu Transform ◽  
Fractional Differential

In this study, we examine adapting and using the Sumudu decomposition method (SDM) as a way to find approximate solutions to two-dimensional fractional partial differential equations and propose a numerical algorithm for solving fractional Riccati equation. This method is a combination of the Sumudu transform method and decomposition method. The fractional derivative is described in the Caputo sense. The results obtained show that the approach is easy to implement and accurate when applied to various fractional differential equations.

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