Research on Stability of Explicit Runge-Kutta Method for Solving Constantly Gradually Varied Flow in Open Trough
Explicit Runge-Kutta method is one of the commonly used algorithms to solve the differential equation of constantly gradually varied flow in open channel, which has been studied and popularized by some domestic scholars in recent years. Studying the stability of explicit Runge-Kutta method to solve...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | zho |
| Published: |
Editorial Office of Pearl River
2021-01-01
|
| Series: | Renmin Zhujiang |
| Subjects: | |
| Online Access: | http://www.renminzhujiang.cn/thesisDetails#10.3969/j.issn.1001-9235.2021.02.013 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841535711819333632 |
|---|---|
| author | ZHOU Bin |
| author_facet | ZHOU Bin |
| author_sort | ZHOU Bin |
| collection | DOAJ |
| description | Explicit Runge-Kutta method is one of the commonly used algorithms to solve the differential equation of constantly gradually varied flow in open channel, which has been studied and popularized by some domestic scholars in recent years. Studying the stability of explicit Runge-Kutta method to solve the constantly gradually varied flow equation in open channel can further consolidate the foundation of technical popularization. The fourth-order explicit Runge-Kutta equation of constantly gradually varied flow in open channel is expanded by Taylor formula of multivariate function, and the error propagation equation can be obtained after omitting high-order trace and eliminating some items. The error propagation equation shows that when the fourth-order explicit Runge-Kutta method is used to solve the differential equation of constantly gradually varied flow in open trough, the slow flow pattern should be calculated from downstream to upstream, and the rapid flow pattern should be calculated from upstream to downstream, so that the stability can be guaranteed when a sufficiently small length is used for calculation. This conclusion can be further verified by typical calculation, and can be further extended to the general explicit Runge-Kutta method. |
| format | Article |
| id | doaj-art-98b2e6661aaf49cd90fb8f11ff36393c |
| institution | Kabale University |
| issn | 1001-9235 |
| language | zho |
| publishDate | 2021-01-01 |
| publisher | Editorial Office of Pearl River |
| record_format | Article |
| series | Renmin Zhujiang |
| spelling | doaj-art-98b2e6661aaf49cd90fb8f11ff36393c2025-01-15T02:29:16ZzhoEditorial Office of Pearl RiverRenmin Zhujiang1001-92352021-01-014247648073Research on Stability of Explicit Runge-Kutta Method for Solving Constantly Gradually Varied Flow in Open TroughZHOU BinExplicit Runge-Kutta method is one of the commonly used algorithms to solve the differential equation of constantly gradually varied flow in open channel, which has been studied and popularized by some domestic scholars in recent years. Studying the stability of explicit Runge-Kutta method to solve the constantly gradually varied flow equation in open channel can further consolidate the foundation of technical popularization. The fourth-order explicit Runge-Kutta equation of constantly gradually varied flow in open channel is expanded by Taylor formula of multivariate function, and the error propagation equation can be obtained after omitting high-order trace and eliminating some items. The error propagation equation shows that when the fourth-order explicit Runge-Kutta method is used to solve the differential equation of constantly gradually varied flow in open trough, the slow flow pattern should be calculated from downstream to upstream, and the rapid flow pattern should be calculated from upstream to downstream, so that the stability can be guaranteed when a sufficiently small length is used for calculation. This conclusion can be further verified by typical calculation, and can be further extended to the general explicit Runge-Kutta method.http://www.renminzhujiang.cn/thesisDetails#10.3969/j.issn.1001-9235.2021.02.013water surface lineconstantly gradually varied flow in open channelstabilityerror analysisRunge-Kutta method |
| spellingShingle | ZHOU Bin Research on Stability of Explicit Runge-Kutta Method for Solving Constantly Gradually Varied Flow in Open Trough Renmin Zhujiang water surface line constantly gradually varied flow in open channel stability error analysis Runge-Kutta method |
| title | Research on Stability of Explicit Runge-Kutta Method for Solving Constantly Gradually Varied Flow in Open Trough |
| title_full | Research on Stability of Explicit Runge-Kutta Method for Solving Constantly Gradually Varied Flow in Open Trough |
| title_fullStr | Research on Stability of Explicit Runge-Kutta Method for Solving Constantly Gradually Varied Flow in Open Trough |
| title_full_unstemmed | Research on Stability of Explicit Runge-Kutta Method for Solving Constantly Gradually Varied Flow in Open Trough |
| title_short | Research on Stability of Explicit Runge-Kutta Method for Solving Constantly Gradually Varied Flow in Open Trough |
| title_sort | research on stability of explicit runge kutta method for solving constantly gradually varied flow in open trough |
| topic | water surface line constantly gradually varied flow in open channel stability error analysis Runge-Kutta method |
| url | http://www.renminzhujiang.cn/thesisDetails#10.3969/j.issn.1001-9235.2021.02.013 |
| work_keys_str_mv | AT zhoubin researchonstabilityofexplicitrungekuttamethodforsolvingconstantlygraduallyvariedflowinopentrough |