Integral Transforms and the Hyers–Ulam Stability of Linear Differential Equations with Constant Coefficients
Integral transform methods are a common tool employed to study the Hyers–Ulam stability of differential equations, including Laplace, Kamal, Tarig, Aboodh, Mahgoub, Sawi, Fourier, Shehu, and Elzaki integral transforms. This work provides improved techniques for integral transforms in relation to est...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/16/2/135 |
| _version_ | 1797296949268840448 |
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| author | Douglas R. Anderson |
| author_facet | Douglas R. Anderson |
| author_sort | Douglas R. Anderson |
| collection | DOAJ |
| description | Integral transform methods are a common tool employed to study the Hyers–Ulam stability of differential equations, including Laplace, Kamal, Tarig, Aboodh, Mahgoub, Sawi, Fourier, Shehu, and Elzaki integral transforms. This work provides improved techniques for integral transforms in relation to establishing the Hyers–Ulam stability of differential equations with constant coefficients, utilizing the Kamal transform, where we focus on first- and second-order linear equations. In particular, in this work, we employ the Kamal transform to determine the Hyers–Ulam stability and Hyers–Ulam stability constants for first-order complex constant coefficient differential equations and, for second-order real constant coefficient differential equations, improving previous results obtained by using the Kamal transform. In a section of examples, we compare and contrast our results favorably with those established in the literature using means other than the Kamal transform. |
| first_indexed | 2024-03-07T22:12:14Z |
| format | Article |
| id | doaj.art-9335ee7d900c4ea5a5bf34211679d214 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-07T22:12:14Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-9335ee7d900c4ea5a5bf34211679d2142024-02-23T15:35:48ZengMDPI AGSymmetry2073-89942024-01-0116213510.3390/sym16020135Integral Transforms and the Hyers–Ulam Stability of Linear Differential Equations with Constant CoefficientsDouglas R. Anderson0Department of Mathematics, Concordia College, Moorhead, MN 56562, USAIntegral transform methods are a common tool employed to study the Hyers–Ulam stability of differential equations, including Laplace, Kamal, Tarig, Aboodh, Mahgoub, Sawi, Fourier, Shehu, and Elzaki integral transforms. This work provides improved techniques for integral transforms in relation to establishing the Hyers–Ulam stability of differential equations with constant coefficients, utilizing the Kamal transform, where we focus on first- and second-order linear equations. In particular, in this work, we employ the Kamal transform to determine the Hyers–Ulam stability and Hyers–Ulam stability constants for first-order complex constant coefficient differential equations and, for second-order real constant coefficient differential equations, improving previous results obtained by using the Kamal transform. In a section of examples, we compare and contrast our results favorably with those established in the literature using means other than the Kamal transform.https://www.mdpi.com/2073-8994/16/2/135Hyers–Ulam stabilityHyers–Ulam constantintegral transformbest constant |
| spellingShingle | Douglas R. Anderson Integral Transforms and the Hyers–Ulam Stability of Linear Differential Equations with Constant Coefficients Symmetry Hyers–Ulam stability Hyers–Ulam constant integral transform best constant |
| title | Integral Transforms and the Hyers–Ulam Stability of Linear Differential Equations with Constant Coefficients |
| title_full | Integral Transforms and the Hyers–Ulam Stability of Linear Differential Equations with Constant Coefficients |
| title_fullStr | Integral Transforms and the Hyers–Ulam Stability of Linear Differential Equations with Constant Coefficients |
| title_full_unstemmed | Integral Transforms and the Hyers–Ulam Stability of Linear Differential Equations with Constant Coefficients |
| title_short | Integral Transforms and the Hyers–Ulam Stability of Linear Differential Equations with Constant Coefficients |
| title_sort | integral transforms and the hyers ulam stability of linear differential equations with constant coefficients |
| topic | Hyers–Ulam stability Hyers–Ulam constant integral transform best constant |
| url | https://www.mdpi.com/2073-8994/16/2/135 |
| work_keys_str_mv | AT douglasranderson integraltransformsandthehyersulamstabilityoflineardifferentialequationswithconstantcoefficients |