Applications of normal S-iterative method to a nonlinear integral equation.
1Department of Mathematics, Faculty of Science and Letters, Yildiz Technical University, Davutpasa Campus, Esenler, 34220 Istanbul, Turkey.
Thescientificworldjournal
|September 4, 2014
Summary
A novel S-iterative method demonstrates convergence for solving complex nonlinear integral equations. Researchers also established a data dependence result, crucial for understanding solution stability in these functional equations.
Area of Science:
- Numerical Analysis
- Applied Mathematics
- Functional Equations
Background:
- Nonlinear integral equations, specifically mixed Volterra-Fredholm types, present significant challenges in theoretical and applied mathematics.
- Understanding the convergence and stability of numerical methods is crucial for obtaining reliable solutions.
Purpose of the Study:
- To investigate the convergence properties of a normal S-iterative method for a specific class of nonlinear integral equations.
- To establish a data dependence result for the solutions of these equations, assessing the impact of input variations.
Main Methods:
- Application of a normal S-iterative method to a mixed type Volterra-Fredholm functional nonlinear integral equation.
- Theoretical analysis to prove convergence of the iterative scheme.
- Development and proof of a data dependence result for the obtained solutions.
Main Results:
- The normal S-iterative method was proven to converge to the solution of the addressed integral equation.
- A data dependence result was successfully established, indicating how solution variations relate to changes in the equation's data.
Conclusions:
- The S-iterative method offers a viable approach for solving this class of nonlinear integral equations.
- The data dependence result provides important insights into the robustness and reliability of the solutions obtained.
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