Modified Sumudu Transform and Its Properties

Duran, Ugur

doi:10.16984/saufenbilder.825180

Cited by 3 publications

(7 citation statements)

References 9 publications

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“…The definitions, characteristics, and theorems of the Sumudu transform scheme that we employed in this work are offered in this section (refer to [29,[45][46][47][48][49][50][51][52]). Definition 1.…”

Section: Sumudu Transform Methodsmentioning

confidence: 99%

Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method

Moltot

Deresse

2022

Advances in Mathematical Physics

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In this study, an efficient analytical method called the Sumudu Iterative Method (SIM) is introduced to obtain the solutions for the nonlinear delay differential equation (NDDE). This technique is a mixture of the Sumudu transform method and the new iterative method. The Sumudu transform method is used in this approach to solve the equation’s linear portion, and the new iterative method’s successive iterative producers are used to solve the equation’s nonlinear portion. Some basic properties and theorems which help us to solve the governing problem using the suggested approach are revised. The benefit of this approach is that it solves the equations directly and reliably, without the prerequisite for perturbations or linearization or extensive computer labor. Five sample instances from the DDEs are given to confirm the method’s reliability and effectiveness, and the outcomes are compared with the exact solution with the assistance of tables and graphs after taking the sum of the first eight iterations of the approximate solution. Furthermore, the findings indicate that the recommended strategy is encouraging for solving other types of nonlinear delay differential equations.

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Section: Sumudu Transform Methodsmentioning

confidence: 99%

Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method

Moltot

Deresse

2022

Advances in Mathematical Physics

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“…According to article [31], the author introduced a transform called "the modified Sumudu transform", which was applied to a number of functions, and its properties were studied. Nevertheless, despite its presented properties, it is possible to investigate whether a convergent series solution can be achieved when it is combined with the MI method for…”

Section: Combination Of the Old Modified Sumudumentioning

confidence: 99%

“…We will demonstrate the use of this combination by solving three systems of NPDEs as examples. We will also present a clear example of a NPDE and demonstrate how to combine the old transformations from [31] with the MI method to obtain convergent solutions to the NPDE.…”

Section: Introductionmentioning

confidence: 99%

“…Section 5 presents three different examples of NPDE systems solved using an appropriate MST method combined with an MI approach, deriving the solutions of the corresponding NPDE system that evaluates the effectiveness of the modified Sumudu-modified iteration (MSMI) method. At last, Section 6 demonstrates how the transformation proposed in [31] can be combined with the MI method to solve a NPDE.…”

Section: Introductionmentioning

confidence: 99%

“…with the ICs ϕ r, 0 = r, ϕ 0, t = 0, 86 and using the transformation mentioned in [31] to eq. ( 85) with utilizing (86), we obtain…”

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confidence: 99%

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Employing a Modified Sumudu with a Modified Iteration Method to Solve the System of Nonlinear Partial Differential Equations

Mustafa

2023

Computational and Mathematical Methods

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The Sumudu transform is presented in this paper in a modified form which is aimed at improving its performance and employing it along with a modified iteration method in order to determine the solution to a system of nonlinear partial differential equations. This includes a theoretical analysis of the associated modified Sumudu transform. It also includes an explanation of the mathematical method for utilizing the transform in conjunction with the modified iteration technique. The iteration method is employed to determine the nonlinear terms of the equations. The research is valuable in the sense that it allows approximate and exact solution configurations to be determined by combining the modified Sumudu transform with a modified iteration method. As another benefit, the modified Sumudu transform can be developed and enhanced to be applicable to a wide range of equations, making it an effective solution tool. By combining techniques, a final advantage is that the solutions can be derived quickly and easily as a result of the combined approach. Finally, an old transformation which has been modified from the Sumudu transform is combined with the modified iteration method to examine its capability of yielding convergent solutions by incorporating the modified iteration method into it.

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Analysis of the nonlinear Fitzhugh–Nagumo equation and its derivative based on the Rabotnov fractional exponential function

Aychluh,

Suthar,

Purohit

2024

Partial Differential Equations in Applied Mathematics

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Modified Sumudu Transform and Its Properties

Cited by 3 publications

References 9 publications

Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method

Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method

Employing a Modified Sumudu with a Modified Iteration Method to Solve the System of Nonlinear Partial Differential Equations

Analysis of the nonlinear Fitzhugh–Nagumo equation and its derivative based on the Rabotnov fractional exponential function

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