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Approximate solution of Urysohn integral equations using the Adomian decomposition method.
Randhir Singh1, Gnaneshwar Nelakanti1, Jitendra Kumar1
1Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India.
Thescientificworldjournal
|February 28, 2014
Summary
The Adomian decomposition method (ADM) offers a direct recursive approach for approximating solutions to Urysohn integral equations. This study demonstrates its accuracy and applicability through numerical examples and convergence analysis.
Area of Science:
- Numerical Analysis
- Integral Equations
- Applied Mathematics
Background:
- Urysohn integral equations are a class of nonlinear integral equations with applications in various scientific fields.
- Approximate analytical solutions are often required due to the complexity of exact solutions.
- The Adomian decomposition method (ADM) is a powerful technique for solving nonlinear equations.
Purpose of the Study:
- To apply the Adomian decomposition method (ADM) for finding approximate series solutions to Urysohn integral equations.
- To establish a direct recursive scheme for efficient approximate solutions.
- To analyze the convergence properties and error bounds of the ADM for these equations.
Main Methods:
- The Adomian decomposition method (ADM) is employed to derive a recursive formula for the series solution.
- Components of the series solution are calculated iteratively.
- Convergence and error analysis are performed theoretically.
Main Results:
- The ADM provides a straightforward recursive scheme for generating approximate series solutions.
- The components of the series solution are easily computable.
- Numerical examples confirm the accuracy and practical utility of the ADM.
Conclusions:
- The Adomian decomposition method is an effective technique for solving Urysohn integral equations.
- The method offers a balance between accuracy and computational simplicity.
- The convergence and error analysis provide theoretical support for the method's reliability.
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