# Coupled ODE Solver

Description| How it works| Planetary MotionThis app solves a system of coupled first order ODEs of the form

**Y**' = f(

**Y**,t), given initial conditions Y(0).

This app can solve upto 10 given equations. This app can also be used to solve a Differential Algrebraic Equations. It can also be used to solve a higher order ODE (upto order 10) by breaking it up into a system of first order ODEs. And finally, it can also be used to solve Partial Differential Equations (PDEs) using the method of lines.

## Download

.xls file (28 KB)## How to use

All cells requiring inputs are coloured light yellow.To provide the inputs to the tool, follow these steps:

1. Key in the number of equations to be solved in cell A8.

2. Key in the initial conditions in the cells B11 downwards.

3. Key in the equations in the cells starting from B23 downwards. The equation must be keyed in using the variable names t, Y1, Y2, Y3,...etc.

For example, to key in the equation

Y(1)' = 2*Y(1)*t,

enter

= 2*Y1*t

in the cell B23.

*The equal to sign is required.*

If correctly entered, the cells will display the value of the derivative at the initial condition.

4. Key in the range of t in the cells B35 and B36.

5. Key in the number of data points required in cells A39. A higher number gives more accuracy, but it takes longer to solve.

Click on the 'Solve' button.

The solution is obtained from cell B43 downwards.

The following screen shot shows the entries for solving the system of differential equations:

Y(1)' = Y(2)

Y(2)' = -Y(1)

from t = 0 to t = 10, with the initial conditions

Y(1) (@ t=0) = 1

Y(2) (@ t=0) = -1

and 100 data points.

## Acknowledgement

I would like to thank Frans van Zelm for spotting and correcting an error with the VBA code in this app.

## Also See:

First order ODE SolverSecond order ODE Solver

Linear Equation Solver

Non-linear Equation Solver