Applications of Double ARA Integral Transform
This paper describes our construction of a new double transform, which we call the double ARA transform (DARAT). Our novel double-integral transform can be used to solve partial differential equations and other problems. We discuss some fundamental characteristics of our approach, including existenc...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/10/12/216 |
| _version_ | 1797460786446073856 |
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| author | Rania Saadeh |
| author_facet | Rania Saadeh |
| author_sort | Rania Saadeh |
| collection | DOAJ |
| description | This paper describes our construction of a new double transform, which we call the double ARA transform (DARAT). Our novel double-integral transform can be used to solve partial differential equations and other problems. We discuss some fundamental characteristics of our approach, including existence, linearity, and several findings relating to partial derivatives and the double convolution theorem. DARAT can be used to precisely solve a variety of partial differential equations, including the heat equation, wave equation, telegraph equation, Klein–Gordon equation, and others, all of which are crucial for physical applications. Herein, we use DARAT to solve model integral equations to obtain exact solutions. We conclude that our novel method is easier to use than comparable transforms. |
| first_indexed | 2024-03-09T17:10:01Z |
| format | Article |
| id | doaj.art-1a93425d30534dc4a00c75a6617dfb18 |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-09T17:10:01Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-1a93425d30534dc4a00c75a6617dfb182023-11-24T14:07:09ZengMDPI AGComputation2079-31972022-12-01101221610.3390/computation10120216Applications of Double ARA Integral TransformRania Saadeh0Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13132, JordanThis paper describes our construction of a new double transform, which we call the double ARA transform (DARAT). Our novel double-integral transform can be used to solve partial differential equations and other problems. We discuss some fundamental characteristics of our approach, including existence, linearity, and several findings relating to partial derivatives and the double convolution theorem. DARAT can be used to precisely solve a variety of partial differential equations, including the heat equation, wave equation, telegraph equation, Klein–Gordon equation, and others, all of which are crucial for physical applications. Herein, we use DARAT to solve model integral equations to obtain exact solutions. We conclude that our novel method is easier to use than comparable transforms.https://www.mdpi.com/2079-3197/10/12/216ARA transformdouble ARA transformpartial differential equations |
| spellingShingle | Rania Saadeh Applications of Double ARA Integral Transform Computation ARA transform double ARA transform partial differential equations |
| title | Applications of Double ARA Integral Transform |
| title_full | Applications of Double ARA Integral Transform |
| title_fullStr | Applications of Double ARA Integral Transform |
| title_full_unstemmed | Applications of Double ARA Integral Transform |
| title_short | Applications of Double ARA Integral Transform |
| title_sort | applications of double ara integral transform |
| topic | ARA transform double ARA transform partial differential equations |
| url | https://www.mdpi.com/2079-3197/10/12/216 |
| work_keys_str_mv | AT raniasaadeh applicationsofdoublearaintegraltransform |