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Theoretical analysis of -transform decomposition method with applications of nonlinear ordinary differentialequations
Nazek A Obeidat1, Mahmoud Saleh Rawashdeh1, Mohammad N Al Smadi1
1Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan.
Science Progress
|May 25, 2024
Summary
This study introduces the -transform Adomian decomposition method for solving nonlinear differential equations. The method proves efficient and adaptable for various equations, offering exact solutions.
Area of Science:
- Mathematics
- Applied Mathematics
- Differential Equations
Background:
- The Riccati differential equation is a significant first-order nonlinear ODE with applications in diverse fields.
- Existing methods for solving nonlinear differential equations can be complex or limited in scope.
Purpose of the Study:
- To introduce and validate the -transform Adomian decomposition method for solving nonlinear differential equations.
- To provide theoretical proofs and demonstrate the method's efficacy through detailed analysis.
Main Methods:
- The study employs the -transform Adomian decomposition method, combining the Adomian decomposition method with the -transform.
- New theorems related to the -transform technique are rigorously proven.
Main Results:
- The -transform Adomian decomposition method is shown to be highly efficient and adaptable for a wide range of linear and nonlinear differential equations.
- Exact solutions obtained using this method are compared favorably with existing literature solutions.
Conclusions:
- The -transform Adomian decomposition method is a powerful and versatile tool for finding exact solutions to nonlinear differential equations.
- The method offers significant advantages in terms of efficiency, utility, and adaptability.
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