Manual rk4

RK4
Version 3.0
(updated 12/1/2006)

©2001, 2005, 2006 Tomas Co Michigan Technological University Houghton, MI 49931

Table of Contents
Description Rationale Special Features Installing the RK4 Add-In Activating/Deactivating RK4 Uninstalling the RK4 Add-In Tutorial Variables and Parameters Application I: Using RK4 Interface to input model directly Application II: Using a text editor tocreate/edit RK4 model file Application IV: Combining Plots in one Chart 6 7 16 27 3 3 3 4 4 4

Application III: Using Solver with RK4 Worksheets 20 Application V. Parameter estimation from combining different data. 36

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Description: An Excel add-in to produce an Excel spreadsheet that renders a fixedinterval, fourth-order Runge Kutta method for solving initial value systems for small tomedium-size simulation studies.

Rationale: Excel spreadsheets are familiar to several PC users. Once rendered, the spreadsheets will contain formulas which the user can later modify using standard Excel commands or enhanced/advanced commands based on other add-ins such as SOLVER to perform further analysis or parameter estimation.

Special Features: 1. Ability to easily attach scroll bars tochosen parameters and initial conditions. This allows the user a quicker interface to perform simulation studies. 2. Ability to open and save model files ( the default file extensions are *.rk4). These files are ordinary text files. Thus, they can be also be created and edited using any text editor such as NOTEPAD or WORDPAD. 3. A simple interface for generating several time-plots or phase planeplots. 4. A simple interface to obtain parameter estimation of models based on combining several data sets. The data sets can have different and non-uniform sampling points.

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Installing the RK4 Add-In: 1. Save the file: rungekutta4_v3.xla in a directory which is relatively permanent. 2. Open the Excel program and make sure at least one workbook is open. 3. Pull-down the [TOOLS] menu and select[ADD-INS…] submenu item. The ADD-INS window should pop out .) 4. Click the [BROWSE…] button, then open the file: rungekutta4_v3.xla 5. Click the [OK] button. (This should activate the RK4 add-in and a command bar should appear on the upper left corner as shown in Figure 1.)

Figure 1. The RK4 Command Bar Activating/Deactivating RK4: 1. Pull-down the [TOOLS] menu and select [ADD-INS…] submenuitem. ( The ADD-INS window should pop out.) 2. Click on box next to the [Rungekutta4_v3] item. A check indicates activation while removing the check will deactivate RK4. 3. Click on [OK] button. If RK4 is activated, the command bar shown in Figure 1 should appear. Uninstalling the RK4 Add-In: 1. First deactivate the RK4 add-in as discussed above. 2. Delete the file: rungekutta4_v3.xla(Alternatively, you could the move the file to a different directory or rename it.) 3. Next, go to [TOOLS] [ADD-INS…] submenu. Try activating the RK4 add-in by clicking on the checkbox. 4. A window should pop-out asking “Cannot find add-in… Delete from list ?” Click on the [Yes] button. 5. Click [OK] on the ADD-INS window. RK4 should then be uninstalled. (To reinstall, go to installing instructions given above.)

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Removing the RK4 Toolbar (for MS Excel 2003): 1. Right-click on the [RK4]-toolbar option button (down-arrow on the right of the button), and then select [Add or Remove Button] [Customize] menu. (see Figure 1a).

Figure 1a. 2. A new window should appear (see Figure 1b). Under the [Toolbars] – tab, drag the scrollbar all the way down and select [RK4]. The check-mark will not change,but the [Delete] button should become enabled. Click [Delete] and click [OK] when prompted. Then click on [Close] to exit the Customize window. (Note: if RK4 had not been uninstalled according to procedure above, then the RK4 toolbar will not be permanently removed.)

Figure 1b.

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Tutorial:
( We recommend strictly following the example inputs in the tutorials including the intentional...