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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MDPI AG
2025-04-01
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| author | Reza Mollapourasl Joseph Siebor |
| author_facet | Reza Mollapourasl Joseph Siebor |
| author_sort | Reza Mollapourasl |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-dae2b54b48a24c5da03f248e8fdab40e |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-dae2b54b48a24c5da03f248e8fdab40e2025-08-20T02:59:11ZengMDPI AGMathematics2227-73902025-04-01139141310.3390/math13091413Numerical Solution of Nonlinear Quadratic Integral Equation of Hammerstein Type Based on Fixed-Point SchemeReza Mollapourasl0Joseph Siebor1Department of Mathematics, Farmingdale State College—SUNY, Farmingdale, NY 11735, USADepartment of Mathematics, Farmingdale State College—SUNY, Farmingdale, NY 11735, USAExistence 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.https://www.mdpi.com/2227-7390/13/9/1413Sinc methodmeasure of noncompactnessfixed-point methodconvergencenonlinear hammerestein integral equation |
| spellingShingle | Reza Mollapourasl Joseph Siebor Numerical Solution of Nonlinear Quadratic Integral Equation of Hammerstein Type Based on Fixed-Point Scheme Mathematics Sinc method measure of noncompactness fixed-point method convergence nonlinear hammerestein integral equation |
| title | Numerical Solution of Nonlinear Quadratic Integral Equation of Hammerstein Type Based on Fixed-Point Scheme |
| title_full | Numerical Solution of Nonlinear Quadratic Integral Equation of Hammerstein Type Based on Fixed-Point Scheme |
| title_fullStr | Numerical Solution of Nonlinear Quadratic Integral Equation of Hammerstein Type Based on Fixed-Point Scheme |
| title_full_unstemmed | Numerical Solution of Nonlinear Quadratic Integral Equation of Hammerstein Type Based on Fixed-Point Scheme |
| title_short | Numerical Solution of Nonlinear Quadratic Integral Equation of Hammerstein Type Based on Fixed-Point Scheme |
| title_sort | numerical solution of nonlinear quadratic integral equation of hammerstein type based on fixed point scheme |
| topic | Sinc method measure of noncompactness fixed-point method convergence nonlinear hammerestein integral equation |
| url | https://www.mdpi.com/2227-7390/13/9/1413 |
| work_keys_str_mv | AT rezamollapourasl numericalsolutionofnonlinearquadraticintegralequationofhammersteintypebasedonfixedpointscheme AT josephsiebor numericalsolutionofnonlinearquadraticintegralequationofhammersteintypebasedonfixedpointscheme |