Integrating Initial Value Problems
This section contains Excel workbooks and tutrorials for solving Ordinary Differential Equations (ODEs) using the 4th Order Runge-Kutta (RK4) technique. You may watch all the turorials so that you can build solution sheets from scratch or you may download one of the workbooks given below and modify it for your problem. The normal form of the ODE is y' = f(t,y), with y(0) given, y may be multidimensional.
4th-order Runge-Kutta Intro--movie illustrating the basic iterative step of RK4. (8:03 min)
4th-order Runge-Kutta Example--movie demonstrating RK4 on a simple ODE. (5:59 min)
4th order Runge-Kutta Workbook I--basic computations in Excel to implement RK4. (12:31 min)
4th order Runge-Kutta Workbook II--extracting and graphing the Excel RK4 solution. (4:20 min)
RK4 first workbook--Excel workbook produced in the above movies.
Using the single state RK4 Integration Workbook--how to use the prebuilt RK4 single state workbook. (4:21 min)
Using the two state RK4 Integration Workbook--how to use the prebuilt RK4 two state workbook. (4:05 min)
Using the twelve state RK4 Integration Workbook--for solving three to twelve state ODEs. (9:01 min)
Download Single State Excel Workbook. (393 KB)
Download Two State Excel Workbook. (598 KB)
Download Twelve State Excel Workbook. (3.26MB)