Spreadsheet Implementation of Numerical and Analytical Solutions to Some Classical Partial Differential Equations
This paper presents the implementation of numerical and analytical solutions of some of the classical partial differential equations using Excel spreadsheets. In particular, the heat equation, wave equation, and Laplace’s equation are presented herein since these equations have well known analytical...
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| Format: | Article |
| Language: | English |
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McMaster University
2016-09-01
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| Series: | Spreadsheets in Education |
| Subjects: | |
| Online Access: | http://epublications.bond.edu.au/ejsie/vol9/iss3/1 |
| _version_ | 1797972606297571328 |
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| author | Mark A Lau |
| author_facet | Mark A Lau |
| author_sort | Mark A Lau |
| collection | DOAJ |
| description | This paper presents the implementation of numerical and analytical solutions of some of the classical partial differential equations using Excel spreadsheets. In particular, the heat equation, wave equation, and Laplace’s equation are presented herein since these equations have well known analytical solutions. The numerical solutions can be easily obtained once the differential equations are discretized via finite differences and then using cell formulas to implement the resulting recursive algorithms and other iterative methods such as the successive over-relaxation (SOR) method. The graphing capabilities of spreadsheets can be exploited to enhance the visualization of the solutions to these equations. Furthermore, using Visual Basic for Applications (VBA) can greatly facilitate the implementation of the analytical solutions to these equations, and in the process, one obtains Fourier series approximations to functions governing initial and/or boundary conditions. |
| first_indexed | 2024-04-11T03:51:11Z |
| format | Article |
| id | doaj.art-b55355a8c2f245d487b47f7372beeb34 |
| institution | Directory Open Access Journal |
| issn | 1448-6156 |
| language | English |
| last_indexed | 2024-04-11T03:51:11Z |
| publishDate | 2016-09-01 |
| publisher | McMaster University |
| record_format | Article |
| series | Spreadsheets in Education |
| spelling | doaj.art-b55355a8c2f245d487b47f7372beeb342023-01-02T02:03:02ZengMcMaster UniversitySpreadsheets in Education1448-61562016-09-01931206Spreadsheet Implementation of Numerical and Analytical Solutions to Some Classical Partial Differential EquationsMark A LauThis paper presents the implementation of numerical and analytical solutions of some of the classical partial differential equations using Excel spreadsheets. In particular, the heat equation, wave equation, and Laplace’s equation are presented herein since these equations have well known analytical solutions. The numerical solutions can be easily obtained once the differential equations are discretized via finite differences and then using cell formulas to implement the resulting recursive algorithms and other iterative methods such as the successive over-relaxation (SOR) method. The graphing capabilities of spreadsheets can be exploited to enhance the visualization of the solutions to these equations. Furthermore, using Visual Basic for Applications (VBA) can greatly facilitate the implementation of the analytical solutions to these equations, and in the process, one obtains Fourier series approximations to functions governing initial and/or boundary conditions.http://epublications.bond.edu.au/ejsie/vol9/iss3/1Heat equationwave equationLaplace equationpartial differential equationsfinite differencessuccessive over-relaxation (SOR) method |
| spellingShingle | Mark A Lau Spreadsheet Implementation of Numerical and Analytical Solutions to Some Classical Partial Differential Equations Spreadsheets in Education Heat equation wave equation Laplace equation partial differential equations finite differences successive over-relaxation (SOR) method |
| title | Spreadsheet Implementation of Numerical and Analytical Solutions to Some Classical Partial Differential Equations |
| title_full | Spreadsheet Implementation of Numerical and Analytical Solutions to Some Classical Partial Differential Equations |
| title_fullStr | Spreadsheet Implementation of Numerical and Analytical Solutions to Some Classical Partial Differential Equations |
| title_full_unstemmed | Spreadsheet Implementation of Numerical and Analytical Solutions to Some Classical Partial Differential Equations |
| title_short | Spreadsheet Implementation of Numerical and Analytical Solutions to Some Classical Partial Differential Equations |
| title_sort | spreadsheet implementation of numerical and analytical solutions to some classical partial differential equations |
| topic | Heat equation wave equation Laplace equation partial differential equations finite differences successive over-relaxation (SOR) method |
| url | http://epublications.bond.edu.au/ejsie/vol9/iss3/1 |
| work_keys_str_mv | AT markalau spreadsheetimplementationofnumericalandanalyticalsolutionstosomeclassicalpartialdifferentialequations |