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Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem
1Department of Mathematics, Amasya University, Ipekköy, Amasya, Turkey.
Springerplus
|December 10, 2016
Summary
This study introduces a novel semi-analytical method using the weighted mean-value theorem to solve Fredholm integral equations. The technique offers significant advantages over existing methods for mathematical analysis and inequality derivation.
Area of Science:
- Mathematical Analysis
- Numerical Methods
Background:
- Mean value theorems are fundamental in mathematics, enabling key inequalities and proofs.
- Integral equations are crucial in various scientific and engineering disciplines.
Purpose of the Study:
- To introduce a semi-analytical method for solving Fredholm integral equations of the second kind.
- To demonstrate the efficacy and advantages of the proposed method.
Main Methods:
- The study employs a semi-analytical approach.
- The core of the method is the weighted mean-value theorem.
Main Results:
- A novel method for solving Fredholm integral equations of the second kind is presented.
- Illustrative examples confirm the method's significant advantages over existing techniques.
Conclusions:
- The proposed semi-analytical method, based on the weighted mean-value theorem, provides an effective tool for solving Fredholm integral equations.
- This approach offers a valuable alternative for mathematical analysis and the derivation of inequalities.
Keywords:
Linear and nonlinear Fredholm integral equationsSystems of Fredholm integral equationsSystems of Fredholm integro-differential equationsWeighted mean value theoremMore Related Videos
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