Approximate solution of Newell-Whitehead-Segel model with time-fractional derivative
Jinxing Liu1, Muhammad Nadeem2, Yahya Alsayyad3
1Faculty of Science, Yibin University, Yibin, China.
Plos One
|July 20, 2023
Summary
This study introduces a novel method combining Sumudu transform and residual power series method (RPSM) for solving the fractional Newell-Whitehead-Segel model. The approach offers an accurate and efficient series solution without complex calculations.
Area of Science:
- Applied Mathematics
- Fractional Calculus
- Nonlinear Dynamics
Background:
- The Newell-Whitehead-Segel model describes phenomena like pattern formation.
- Solving fractional-order models is crucial for understanding complex systems.
- Existing methods often involve significant computational complexity.
Purpose of the Study:
- To develop an efficient approximate analytical solution for the fractional Newell-Whitehead-Segel model.
- To utilize the Sumudu transform and residual power series method (RPSM).
- To demonstrate the accuracy and applicability of the proposed scheme.
Main Methods:
- Application of Sumudu transform to decompose fractional derivatives.
- Derivation of a recurrence relation.
- Utilizing the residual power series method (RPSM) for series solution generation.
- Iterative computation using initial conditions.
Main Results:
- An accurate series-based approximate solution was successfully derived.
- The method proved effective for the fractional Newell-Whitehead-Segel model.
- The approach avoids complex calculations and restrictions.
- Graphical representations (2D and 3D) illustrate the model's physical behavior.
Conclusions:
- The combined Sumudu transform and RPSM is a powerful and efficient technique for solving fractional nonlinear models.
- The developed method offers high accuracy and validity.
- The findings contribute to the analytical treatment of fractional differential equations.
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