A universal method of solving differential equations in spreadsheet software
We propose a method for solving differential equations implicitly using iterative calculations in spreadsheet software. This method uses difference equations by discretizing the coordinates of the independent variables with cells of spreadsheet for analysis. Thus, the equations are embedded in the c...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | Japanese |
| Published: |
The Japan Society of Mechanical Engineers
2022-11-01
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| Series: | Nihon Kikai Gakkai ronbunshu |
| Subjects: | |
| Online Access: | https://www.jstage.jst.go.jp/article/transjsme/88/916/88_22-00198/_pdf/-char/en |
| _version_ | 1797977057849769984 |
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| author | Kiyomi YAMANE Kouta YUASA Kouki ITO Tasuku KOSUNA Chikashi TAKEMURA |
| author_facet | Kiyomi YAMANE Kouta YUASA Kouki ITO Tasuku KOSUNA Chikashi TAKEMURA |
| author_sort | Kiyomi YAMANE |
| collection | DOAJ |
| description | We propose a method for solving differential equations implicitly using iterative calculations in spreadsheet software. This method uses difference equations by discretizing the coordinates of the independent variables with cells of spreadsheet for analysis. Thus, the equations are embedded in the cells performing substitution of grid point. In addition, the embedded equations are solved by Newton’s method, and the iterative function of the spreadsheet software is used in the calculation. This method can be applied even when the differential equation is discretized by an implicit solution method. Therefore, it can be applied to ordinary and partial differential equations of different types. The advantages of discretization using the implicit method (high computational accuracy, large time increments) are also presented in this paper. The analysis procedure is almost the same regardless of the type of equation. In this paper, as an example, a simple differential equation was analyzed using Microsoft Excel, a typical spreadsheet software, to illustrate the method. The results are also shown by the analysis of the gas lubrication equation. |
| first_indexed | 2024-04-11T05:00:52Z |
| format | Article |
| id | doaj.art-5fe97b09523e440fb2cf45c1f325845c |
| institution | Directory Open Access Journal |
| issn | 2187-9761 |
| language | Japanese |
| last_indexed | 2024-04-11T05:00:52Z |
| publishDate | 2022-11-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Nihon Kikai Gakkai ronbunshu |
| spelling | doaj.art-5fe97b09523e440fb2cf45c1f325845c2022-12-26T01:09:01ZjpnThe Japan Society of Mechanical EngineersNihon Kikai Gakkai ronbunshu2187-97612022-11-018891622-0019822-0019810.1299/transjsme.22-00198transjsmeA universal method of solving differential equations in spreadsheet softwareKiyomi YAMANE0Kouta YUASA1Kouki ITO2Tasuku KOSUNA3Chikashi TAKEMURA4Department of Mechanical Engineering, National Institute of Technology, Matsue CollegeDepartment of Mechanical Engineering, National Institute of Technology, Matsue CollegeDepartment of Mechanical Engineering, National Institute of Technology, Matsue CollegeMolten CorporationIzumo Murata Manufacturing Co., Ltd.We propose a method for solving differential equations implicitly using iterative calculations in spreadsheet software. This method uses difference equations by discretizing the coordinates of the independent variables with cells of spreadsheet for analysis. Thus, the equations are embedded in the cells performing substitution of grid point. In addition, the embedded equations are solved by Newton’s method, and the iterative function of the spreadsheet software is used in the calculation. This method can be applied even when the differential equation is discretized by an implicit solution method. Therefore, it can be applied to ordinary and partial differential equations of different types. The advantages of discretization using the implicit method (high computational accuracy, large time increments) are also presented in this paper. The analysis procedure is almost the same regardless of the type of equation. In this paper, as an example, a simple differential equation was analyzed using Microsoft Excel, a typical spreadsheet software, to illustrate the method. The results are also shown by the analysis of the gas lubrication equation.https://www.jstage.jst.go.jp/article/transjsme/88/916/88_22-00198/_pdf/-char/ennumerical simulationdifferential equationspreadsheet softwareengineering educationnewton’s methodlubrication equation |
| spellingShingle | Kiyomi YAMANE Kouta YUASA Kouki ITO Tasuku KOSUNA Chikashi TAKEMURA A universal method of solving differential equations in spreadsheet software Nihon Kikai Gakkai ronbunshu numerical simulation differential equation spreadsheet software engineering education newton’s method lubrication equation |
| title | A universal method of solving differential equations in spreadsheet software |
| title_full | A universal method of solving differential equations in spreadsheet software |
| title_fullStr | A universal method of solving differential equations in spreadsheet software |
| title_full_unstemmed | A universal method of solving differential equations in spreadsheet software |
| title_short | A universal method of solving differential equations in spreadsheet software |
| title_sort | universal method of solving differential equations in spreadsheet software |
| topic | numerical simulation differential equation spreadsheet software engineering education newton’s method lubrication equation |
| url | https://www.jstage.jst.go.jp/article/transjsme/88/916/88_22-00198/_pdf/-char/en |
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