A direct method to calculate characteristic forms
We propose a method to obtain characteristic curves, Riemann variables, and characteristic forms for a partial differential system of hyperbolic waves and a first order quasi-linear partial differential equations. The method is based on a construction of a left eigenvector of a matrix from eigenvalu...
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| Format: | Article |
| Language: | English |
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Elsevier
2022-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818122000262 |
| _version_ | 1811241001774219264 |
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| author | Junrong Liu |
| author_facet | Junrong Liu |
| author_sort | Junrong Liu |
| collection | DOAJ |
| description | We propose a method to obtain characteristic curves, Riemann variables, and characteristic forms for a partial differential system of hyperbolic waves and a first order quasi-linear partial differential equations. The method is based on a construction of a left eigenvector of a matrix from eigenvalues of the matrix and some auxiliary matrixes, or some determinants. When applying to a system with no more than 4 dependent variable, the proposed method is numerically stable. An example of flood waves shows how to apply the proposed method. |
| first_indexed | 2024-04-12T13:29:24Z |
| format | Article |
| id | doaj.art-69f93738a9bf44058b66b1f525182c55 |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-04-12T13:29:24Z |
| publishDate | 2022-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-69f93738a9bf44058b66b1f525182c552022-12-22T03:31:13ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812022-06-015100308A direct method to calculate characteristic formsJunrong Liu0School of Mathematics, Northwest University, Xi’an, 710127, Shaanxi, PR ChinaWe propose a method to obtain characteristic curves, Riemann variables, and characteristic forms for a partial differential system of hyperbolic waves and a first order quasi-linear partial differential equations. The method is based on a construction of a left eigenvector of a matrix from eigenvalues of the matrix and some auxiliary matrixes, or some determinants. When applying to a system with no more than 4 dependent variable, the proposed method is numerically stable. An example of flood waves shows how to apply the proposed method.http://www.sciencedirect.com/science/article/pii/S2666818122000262Cramer ruleHyperbolic wavesCharacteristic curvesRiemann variables |
| spellingShingle | Junrong Liu A direct method to calculate characteristic forms Partial Differential Equations in Applied Mathematics Cramer rule Hyperbolic waves Characteristic curves Riemann variables |
| title | A direct method to calculate characteristic forms |
| title_full | A direct method to calculate characteristic forms |
| title_fullStr | A direct method to calculate characteristic forms |
| title_full_unstemmed | A direct method to calculate characteristic forms |
| title_short | A direct method to calculate characteristic forms |
| title_sort | direct method to calculate characteristic forms |
| topic | Cramer rule Hyperbolic waves Characteristic curves Riemann variables |
| url | http://www.sciencedirect.com/science/article/pii/S2666818122000262 |
| work_keys_str_mv | AT junrongliu adirectmethodtocalculatecharacteristicforms AT junrongliu directmethodtocalculatecharacteristicforms |