Sumudu transform: a new integral transform to solve differential equations and control engineering problems

1993 ◽  
Vol 24 (1) ◽  
pp. 35-43 ◽  
Author(s):  
G. K. Watugala
Keyword(s):  
Differential Equations ◽  
Integral Transform ◽  
Control Engineering ◽  
Engineering Problems ◽  
Sumudu Transform ◽  
And Control

scholarly journals On a New Integral Transform and Differential Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
A. Kiliçman ◽  
H. Eltayeb
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Integral Transform ◽  
System Of Differential Equations ◽  
Transform Method ◽  
Control Engineering ◽  
Linear Ordinary Differential Equations ◽  
Sumudu Transform ◽  
Integral Transform Method

Integral transform method is widely used to solve the several differential equations with the initial values or boundary conditions which are represented by integral equations. With this purpose, the Sumudu transform was introduced as a new integral transform by Watugala to solve some ordinary differential equations in control engineering. Later, it was proved that Sumudu transform has very special and useful properties. In this paper we study this interesting integral transform and its efficiency in solving the linear ordinary differential equations with constant and nonconstant coefficients as well as system of differential equations.

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.

Fuzzy Sumudu Transform Approach to Solving Fuzzy Differential Equations With Z-Numbers

2019 ◽  
pp. 18-48 ◽  
Author(s):  
Raheleh Jafari ◽  
Sina Razvarz ◽  
Alexander Gegov ◽  
Satyam Paul ◽  
Sajjad Keshtkar
Keyword(s):  
Nonlinear Systems ◽  
Theoretical Analysis ◽  
Differential Equations ◽  
Fuzzy Numbers ◽  
Euler Method ◽  
Uncertain Nonlinear Systems ◽  
Engineering Problems ◽  
Sumudu Transform ◽  
Simulation Results

Uncertain nonlinear systems can be modeled with fuzzy differential equations (FDEs) and the solutions of these equations are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs. In this book chapter, the solutions of FDEs are approximated by utilizing the fuzzy Sumudu transform (FST) method. Here, the uncertainties are in the sense of fuzzy numbers and Z-numbers. Important theorems are laid down to illustrate the properties of FST. This new technique is compared with Average Euler method and Max-Min Euler method. The theoretical analysis and simulation results show that the FST method is effective in estimating the solutions of FDEs.

scholarly journals Solution of Integral Differential Equations by New Double Integral Transform (Laplace–Sumudu Transform)

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Shams A. Ahmed ◽  
Tarig M. Elzaki ◽  
Abdelgabar Adam Hassan
Keyword(s):  
Differential Equations ◽  
Integral Transform ◽  
Convolution Theorem ◽  
Double Integral ◽  
Sumudu Transform ◽  
Integral Differential Equations

The primary purpose of this research is to demonstrate an efficient replacement double transform named the Laplace–Sumudu transform (DLST) to unravel integral differential equations. The theorems handling fashionable properties of the Laplace–Sumudu transform are proved; the convolution theorem with an evidence is mentioned; then, via the usage of these outcomes, the solution of integral differential equations is built.

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 On optimal boundary and distributed control of partial integro–differential equations

2014 ◽  
Vol 24 (1) ◽  
pp. 5-25 ◽  
Author(s):  
Asatur Zh. Khurshudyan
Keyword(s):  
Differential Equations ◽  
Control Problem ◽  
Integral Transform ◽  
Control Function ◽  
Sufficient Conditions ◽  
Control Process ◽  
Problem Solution ◽  
Control Functions ◽  
Minimization Procedure ◽  
And Control

Abstract A method of optimal control problems investigation for linear partial integro-differential equations of convolution type is proposed, when control process is carried out by boundary functions and right hand side of equation. Using Fourier real generalized integral transform control problem solution is reduced to minimization procedure of chosen optimality criterion under constraints of equality type on desired control function. Optimality of control impacts is obtained for two criteria, evaluating their linear momentum and total energy. Necessary and sufficient conditions of control problem solvability are obtained for both criteria. Numerical calculations are done and control functions are plotted for both cases of control process realization.

Averaging theory for fractional differential equations

2021 ◽  
Vol 24 (2) ◽  
pp. 621-640
Author(s):  
Guanlin Li ◽  
Brad Lehman
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Applied Mathematics ◽  
Time Intervals ◽  
Control Engineering ◽  
Averaged Equations ◽  
Capacitor Voltage ◽  
Engineering Problems ◽  
Fractional Differential ◽  
Autonomous Differential Equations

Abstract The theory of averaging is a classical component of applied mathematics and has been applied to solve some engineering problems, such as in the filed of control engineering. In this paper, we develop a theory of averaging on both finite and infinite time intervals for fractional non-autonomous differential equations. The closeness of the solutions of fractional no-autonomous differential equations and the averaged equations has been proved. The main results of the paper are applied to the switched capacitor voltage inverter modeling problem which is described by the fractional differential equations.

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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