Numerical Solution of Nonlinear Quadratic Integral Equation of Hammerstein Type Based on Fixed-Point Scheme
Existence of the solution for the nonlinear quadratic integral equation of the Hammerstein type in the Banach space BC(<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-04-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/9/1413 |
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| Summary: | Existence of the solution for the nonlinear quadratic integral equation of the Hammerstein type in the Banach space BC(<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">R</mi><mo>+</mo></msub></semantics></math></inline-formula>) has been proved by using the technique of measure of noncompactness and fixed-point theorem. In this article, we obtain an approximate solution for the quadratic integral equation by using the Sinc method and the fixed-point technique. Moreover, the convergence of the numerical scheme for the solution of the integral equation is demonstrated by a theorem, and numerical experiments are presented to show the accuracy of the numerical scheme and guarantee the analytical results. |
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| ISSN: | 2227-7390 |