THE USE OF EXCEL TO TEACH COMPUTER METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS
Universidad Politécnica de Madrid (SPAIN)
About this paper:
Appears in: ICERI2009 Proceedings
Publication year: 2009
Conference name: 2nd International Conference of Education, Research and Innovation
Dates: 16-18 November, 2009
Location: Madrid, Spain
Abstract:The object of this paper is to show the purposefulness, from a didactic point of view, of Excel spreadsheets for the application of different numerical methods to solving initial value problems in ordinary differential equations.
The basic approach is to start from a specific initial value problem and try to obtain an approximated value of the solution in a certain point. This is done by applying different numerical formulas, using an Excel spreadsheet as an implementation tool.
Different step lengths h are considered with the purpose of verifying the convergence of each of the methods applied, beginning by a certain value and successively dividing h by two until a suitable approximation will be obtained.
By applying the different numerical methods to the proposed problem it is possible to compare the convergence speed of the different methods applied.
By analysing the results obtained in the Excel sheets, it is possible to directly obtain boundary marks of the error incurred by each of the different methods applied, without a prior knowledge of the exact solution of the problem.
The Excel sheets that have been built this way offer great easiness as well as high accuracy and speed of calculation, and can help the student to better understand the theoretical concept of convergence of a numerical method. In addition, the use of an Excel spreadsheet also allows the student to actively take part in the resolution of the problem, thus making it easier and encourages him to create his own Excel spreadsheets, with other initial value problems and other numerical methods for its resolution.
Keywords: numerical analysis, runge kutta methods, excel spreadsheets.