An Approximation Method to Compute Highly Oscillatory Singular Fredholm Integro-Differential Equations
This paper appertains the presentation of a Clenshaw–Curtis rule to evaluate highly oscillatory Fredholm integro-differential equations (FIDEs) with Cauchy and weak singularities. To calculate the singular integral, the unknown function approximated by an interpolation polynomial is rewritten as a T...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/19/3628 |
| _version_ | 1797478164565327872 |
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| author | SAIRA Wen-Xiu Ma |
| author_facet | SAIRA Wen-Xiu Ma |
| author_sort | SAIRA |
| collection | DOAJ |
| description | This paper appertains the presentation of a Clenshaw–Curtis rule to evaluate highly oscillatory Fredholm integro-differential equations (FIDEs) with Cauchy and weak singularities. To calculate the singular integral, the unknown function approximated by an interpolation polynomial is rewritten as a Taylor series expansion. A system of linear equations of FIDEs obtained by using equally spaced points as collocation points is solved to obtain the unknown function. The proposed method attains higher accuracy rates, which are proven by error analysis and some numerical examples as well. |
| first_indexed | 2024-03-09T21:28:06Z |
| format | Article |
| id | doaj.art-f62e939a56fe480c9222ce5082db39fe |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T21:28:06Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f62e939a56fe480c9222ce5082db39fe2023-11-23T21:04:49ZengMDPI AGMathematics2227-73902022-10-011019362810.3390/math10193628An Approximation Method to Compute Highly Oscillatory Singular Fredholm Integro-Differential EquationsSAIRA0Wen-Xiu Ma1Department of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaDepartment of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaThis paper appertains the presentation of a Clenshaw–Curtis rule to evaluate highly oscillatory Fredholm integro-differential equations (FIDEs) with Cauchy and weak singularities. To calculate the singular integral, the unknown function approximated by an interpolation polynomial is rewritten as a Taylor series expansion. A system of linear equations of FIDEs obtained by using equally spaced points as collocation points is solved to obtain the unknown function. The proposed method attains higher accuracy rates, which are proven by error analysis and some numerical examples as well.https://www.mdpi.com/2227-7390/10/19/3628Clenshaw–Curtis rulehighly oscillatory integralsTaylor seriesweak singularitiesCauchy singularitycollocation method |
| spellingShingle | SAIRA Wen-Xiu Ma An Approximation Method to Compute Highly Oscillatory Singular Fredholm Integro-Differential Equations Mathematics Clenshaw–Curtis rule highly oscillatory integrals Taylor series weak singularities Cauchy singularity collocation method |
| title | An Approximation Method to Compute Highly Oscillatory Singular Fredholm Integro-Differential Equations |
| title_full | An Approximation Method to Compute Highly Oscillatory Singular Fredholm Integro-Differential Equations |
| title_fullStr | An Approximation Method to Compute Highly Oscillatory Singular Fredholm Integro-Differential Equations |
| title_full_unstemmed | An Approximation Method to Compute Highly Oscillatory Singular Fredholm Integro-Differential Equations |
| title_short | An Approximation Method to Compute Highly Oscillatory Singular Fredholm Integro-Differential Equations |
| title_sort | approximation method to compute highly oscillatory singular fredholm integro differential equations |
| topic | Clenshaw–Curtis rule highly oscillatory integrals Taylor series weak singularities Cauchy singularity collocation method |
| url | https://www.mdpi.com/2227-7390/10/19/3628 |
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