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 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 Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Raheel Kamal ◽  
Kamran ◽  
Gul Rahmat ◽  
Ali Ahmadian ◽  
Noreen Izza Arshad ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Meshless Method ◽  
Inverse Laplace Transform ◽  
Contour Integral ◽  
Partial Differential ◽  
One Dimensional ◽  
The Laplace Transform

AbstractIn this article we propose a hybrid method based on a local meshless method and the Laplace transform for approximating the solution of linear one dimensional partial differential equations in the sense of the Caputo–Fabrizio fractional derivative. In our numerical scheme the Laplace transform is used to avoid the time stepping procedure, and the local meshless method is used to produce sparse differentiation matrices and avoid the ill conditioning issues resulting in global meshless methods. Our numerical method comprises three steps. In the first step we transform the given equation to an equivalent time independent equation. Secondly the reduced equation is solved via a local meshless method. Finally, the solution of the original equation is obtained via the inverse Laplace transform by representing it as a contour integral in the complex left half plane. The contour integral is then approximated using the trapezoidal rule. The stability and convergence of the method are discussed. The efficiency, efficacy, and accuracy of the proposed method are assessed using four different problems. Numerical approximations of these problems are obtained and validated against exact solutions. The obtained results show that the proposed method can solve such types of problems efficiently.

scholarly journals Exact solution of time-fractional partial differential equations using Laplace transform

2016 ◽  
Vol 5 (1) ◽  
pp. 86
Author(s):  
Naser Al-Qutaifi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Partial Differential Equations ◽  
Laplace Transform Method ◽  
Partial Differential ◽  
Transform Method ◽  
Integer Order ◽  
First Derivative ◽  
The Laplace Transform

<p>The idea of replacing the first derivative in time by a fractional derivative of order , where , leads to a fractional generalization of any partial differential equations of integer order. In this paper, we obtain a relationship between the solution of the integer order equation and the solution of its fractional extension by using the Laplace transform method.</p>

scholarly journals Laplace–Elzaki Transform and its Properties with Applications to Integral and Partial Differential Equations: تحويل لابلاس-الزاكي وخواصه مع تطبيقاته على المعادلات التكاملية والتفاضلية الجزئية

2019 ◽  
Vol 3 (2) ◽  
Author(s):  
Safaa Adnan Shaikh Al-Sook, Mohammad Mahmud Amer
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Integral Transform ◽  
Convolution Theorem ◽  
Double Integral ◽  
Partial Differential ◽  
Function Of Two Variables

  Laplace-Elzaki transform (LET) as a double integral transform of a function  of two variables was presented to solve some integral and partial differential equations. Main properties and theorems were proved. The convolution of two function  and  and the convolution theorem were discussed. The integral and partial differential equations were turned to algebraic ones by using (LET) and its properties. The results showed that the Laplace-Elzaki transform was more efficient and useful to handle such these kinds of equations.    

The Combined Laplace-Variational Iteration Method for Partial Differential Equations

2013 ◽  
Vol 14 (2) ◽  
Author(s):  
M. Matinfar ◽  
M. Saeidy ◽  
M. Ghasemi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Partial Differential ◽  
Transform Method ◽  
Variational Iteration ◽  
Approximate Analytical Solutions ◽  
The Laplace Transform

AbstractIn this paper, the Laplace transform Variational Iteration Method (LVIM) is employed to obtain approximate analytical solutions of the linear and nonlinear partial differential equations. This method is a combined form of the Laplace transform method and the Variational Iteration Method. The proposed scheme, finds the solutions without any discretization or restrictive assumptions and is free from round-off errors and therefore, reduces the numerical computations to a great extent. Some illustrative examples are presented and the numerical results show that the solutions of the LVIM are in good agreement with the exact solution.

scholarly journals Solution of One-dimensional Partial Differential Equation with Higher-Order Derivative by Double Laplace Transform Method

2021 ◽  
Vol 4 (3) ◽  
pp. 1-11
Author(s):  
Anongo D.O. ◽  
Awari Y.S.
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Integral Transform ◽  
Higher Order ◽  
Laplace Transform Method ◽  
Partial Differential ◽  
Transform Method ◽  
Double Laplace Transform ◽  
Engineering Sciences

Many problems in natural and engineering sciences such as heat transfer, elasticity, quantum mechanics, water flow, and others are modelled mathematically by partial differential equations. Some of these problems may be linear, nonlinear, homogeneous, non-homogeneous, and order greater or equal one. Finding the theoretical solution to these problems with less cumbersome techniques is an active area of research in the aforementioned field. In this research paper, we have developed a new application of the double Laplace transform method to solve homogeneous and non-homogeneous linear partial differential equations (pdes) with higher-order derivatives (i.e order n where n≥2) in science and engineering. We discussed a brief theory of double Laplace transforms that helped in its application. The main advantage of our method is the reduction of computational effort in finding solution to pdes. Another major benefit of our method is solving problems in the form of (21) directly by transforming to an algebraic equation where the inverse double Laplace transform is implemented for analytical solution, unlike other integral transform methods that would first transform to a system of ODEs before they are solved, is it also very effective in solving linear high-order partial differential equations and yield fast convergence. We present a well-simplified solution for easier comprehension by upcoming researchers.

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.

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