The Computable Differential Equation Lecture ... - Bruce E. Shapiro

182 CHAPTER 9. DIFFERENTIAL ALGEBRAIC EQUATIONS
In practice it is better not to compute the inverse, but instead to use a linear solver
to compute the update, however, this program is for illustrative purposes and the
inverse is sufficient. Finally, we can implement the solver. Of course we also need
to give values to the parameters α, β, γ.
{A n , B n , X n , e n } = {1, 0, 0, 1};
h = 0.01;
α=10; β=γ=1;
data = {{0, A n , B n , X n , e n }};
For[t = 0, t < 3, t += h,
{A n , B n ,X n , e n } = nextStep[h, {A n , B n , X n , e n }];
data = Append[data, {t+h, A n , B n , X n , e n }];
];
This will generate a table of values of ordered sets of values {{t 0 , A 0 , B 0 , X 0 , e 0 }, {t 1 , A 1 , B 1 , X 1 , e 1 }, . . .
at each of the mesh points. To see the data we could type
TableForm[data]
Mathematica would respond with (only some of the data is shown):
0 1 0 0 1
0.01 0.916713 0.0824626 0.000824626 0.917537
0.02 0.84639 0.151273 0.00233735 0.0848727
. etc
To plot all the curves on a single graph using ListPlot we write the function
plotDataTable,
plotDataTable[d ,styles ] := Module[{nvars, makedata, plt, data,
plots},
nvars = Length[d[[1]]] - 1;
data = Transpose[d];
makedata[i ] := {data[[1]], data[[i + 1]]};
plt[i ] := ListPlot[makedata[i]
Transpose, PlotJoined -> True, PlotStyle -> styles[[i]],
DisplayFunction -> Identity];
plots = plt /@ Range[nvars];
Show[plots, DisplayFunction -> $DisplayFunction];
]
The to actually generate the plot,
plotDataTable[data,
{{Red, Dashing[{.006, 0.008}]},
{Blue, Thickness[.006], Dashing[{0.01}]},
{Green, Thickness[.005]},
Purple}]
Math 582B, Spring 2007
California State University Northridge
c○2007, B.E.Shapiro
Last revised: May 23, 2007