You can solve the following system numerically by entering the equations into a 6×1 matrix and choosing Numeric from the Solve ODE submenu. Three functions x, y, and z are returned as output.
Solve ODE + Numeric
, Functions defined: x, y, z
x′ = x + y - z y′ = - x + y + z z′ = - x - y + z x(0) = 1 y(0) = 1 z(0) = 1
The following table lists values of x, y, and z as the independent variable t varies from 0 to 1.
t | x | y | z |
0 | 1.0000 | 1.0000 | 1.0000 |
.1 | 1.1158 | 1.0938 | .8842 |
.2 | 1.2668 | 1.1695 | .7332 |
.3 | 1.4582 | 1.2173 | .5418 |
.4 | 1.6953 | 1.2253 | .3047 |
.5 | 1.9830 | 1.1791 | .0170 |
.6 | 2.3256 | 1.0619 | - .3256 |
.7 | 2.7265 | .8542 | - .7265 |
.8 | 3.1873 | .5344 | -1.1873 |
.9 | 3.7077 | .0777 | -1.7077 |
1.0 | 4.2842 | - .5424 | -2.2842 |
You can create a matrix with these values as follows.
You can also take advantage of the fact that you are using a word processor to put the values into a 12 by 4 table. You can then revise the table to add lines.