My question is straightforward: How do I convert a continuous function into a discrete-valued function?
The function I want to convert is the JacobiAmplitude function:
\[Phi][t_]ϕ[t_] =
With[{k = 1.01}, JacobiAmplitude[k t, k^-3]];
Plot[\[Phi][t]
Plot[ϕ[t], {t, 0, 50}]
I am using RSolveRSolve
to solve a second-order difference equation and want to add a discrete-time version of the JacobiAmplitudeJacobiAmplitude
function to the model as a forcing term.
I'd like to put a discrete-time JacobiAmplitudeJacobiAmplitude
function, [Phi][n]ϕ[n], into the following difference equation:
RSolve[
{y[n + 2] - y[n + 1] + 0.99*y[n] == \[Phi][n]ϕ[n], {y[0] == 0,
y[1] == 1, \[Phi][0]ϕ[0] == 0}},
y[n], n];n
ListPlot[Transpose@Table[];
ListPlot[
Transpose@Table[{y[n]} /. First[%],
{n, 0, 350}],
Joined -> True, PlotRange -> All]All
]
I'd immensely appreciate any assistance.
Thanks.