Article
| Title: | High accuracy numerical methods for solving second order nonlinear Fredholm integro-differential equations (English) |
| Author: | Dang, Quang A |
| Author: | Nguyen, Thi Thu Ha |
| Author: | Vu, Vinh Quang |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 71 |
| Issue: | 5 |
| Year: | 2026 |
| Pages: | 673-692 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We develop high-order numerical methods for solving second-order nonlinear Fredholm Integro-Differential Equations (FrIDEs). First, we establish the existence and uniqueness of solutions under easily verified conditions and propose a continuous iterative method. Subsequently, we construct a discrete iterative scheme by discretizing this continuous method using the trapezoidal quadrature formula augmented with correction terms. We rigorously prove that the proposed numerical method achieves eighth-order convergence. Extensive experiments on both linear and nonlinear equations demonstrate that our method attains eighth-order accuracy, surpassing existing methods whose accuracy does not exceed fifth order. (English) |
| Keyword: | second order integro-differential equation |
| Keyword: | trapezoidal quadrature formula with corrections |
| Keyword: | iterative method |
| Keyword: | high accuracy numerical method |
| MSC: | 45J05 |
| MSC: | 65L10 |
| MSC: | 65R20 |
| DOI: | 10.21136/AM.2026.0274-25 |
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| Date available: | 2026-10-12T12:59:01Z |
| Last updated: | 2026-10-19 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153798 |
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