Fourth-Order Runge-Kutta Method

The 4th-Order Runge-Kutta method is a very common numerical method used to solve differential equations with a known initial condition. The method starts at the initial condition and proceeds stepwise to develop successive points in the function based on the previous point and the calculated Runge-Kutta parameters. The method lends itself to spreadsheet calculations. I am sure that many others have already developed spreadsheets for this applications.

This spreadsheet that I have developed shows the clever use of Excel's user-defined functions. The user of this spreadsheet can easily change the function being solved in a single location rather than changing every formula in the Excel table. The table can be easily expanded by copying the bottom row of the table into rows below. The spreadsheet also includes a simple graph.

Variable Volume/Concentration Tank Problem: To demonstrate the use of the Runge-Kutta method, two spreadsheets are included that solve the classic chemical engineering tank problem. These problems involve concentration and/or volume varying with time in a tank and require a material balance to derive a differential equation.

This problem is very common on the Chemical Engineering P.E. exam. However, without a computer, the test taker would probably want to solve the differential equations analytically for speed although a numerical solution may be possible on a programmable calculator.

The first spreadsheet has a simple example of concentration declining with time. The problem in the second spreadsheet is more complex in that both concentration and volume vary.

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