A pertinent approach to solve nonlinear fuzzy integro-differential equations
S Narayanamoorthy1, S P Sathiyapriya1
1Department of Mathematics, Bharathiar University, Coimbatore, TamilNadu 641046 India.
Springerplus
|April 28, 2016
Summary
This study introduces a new computational method for solving fuzzy integro-differential equations. The homotopy perturbation method provides accurate and efficient solutions for these complex mathematical problems.
Area of Science:
- Fuzzy Mathematics
- Numerical Analysis
Background:
- Fuzzy integro-differential equations are crucial in fuzzy analysis with applications in analytical dynamics.
- Solving these equations requires efficient computational algorithms.
Purpose of the Study:
- To propose an applicable approach for solving nonlinear fuzzy integro-differential equations.
- To demonstrate the accuracy and efficiency of the homotopy perturbation method.
Main Methods:
- Utilizing parametric forms of fuzzy numbers.
- Applying the homotopy perturbation method.
- Conducting stability and convergence analysis.
Main Results:
- The proposed method yields highly accurate solutions with reduced computational effort.
- Numerical examples confirm the convergence and validity of the technique.
- Comparison with exact solutions and graphical representations validate the approach.
Conclusions:
- The homotopy perturbation method is an effective technique for solving nonlinear fuzzy integro-differential equations.
- The method offers a reliable and efficient approach for theoretical and practical applications.
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