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m_goldberg
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How to sample Sampling a continuous function to create sequence of discrete values?

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MarcoB
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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.

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_] = 
 With[{k = 1.01}, JacobiAmplitude[k t, k^-3]]; 
Plot[\[Phi][t], {t, 0, 50}]

I am using RSolve to solve a second-order difference equation and want to add a discrete-time version of the JacobiAmplitude function to the model as a forcing term.

I'd like to put a discrete-time JacobiAmplitude function, [Phi][n], into the following difference equation:

RSolve[{y[n + 2] - y[n + 1] + 0.99*y[n] == \[Phi][n], {y[0] == 0, 
    y[1] == 1, \[Phi][0] == 0}}, y[n], n];
ListPlot[Transpose@Table[{y[n]} /. First[%], {n, 0, 350}], 
 Joined -> True, PlotRange -> All]

I'd immensely appreciate any assistance.

Thanks.

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:

ϕ[t_] = With[{k = 1.01}, JacobiAmplitude[k t, k^-3]]; 

Plot[ϕ[t], {t, 0, 50}]

I am using RSolve to solve a second-order difference equation and want to add a discrete-time version of the JacobiAmplitude function to the model as a forcing term.

I'd like to put a discrete-time JacobiAmplitude function, ϕ[n], into the following difference equation:

RSolve[
 {y[n + 2] - y[n + 1] + 0.99*y[n] == ϕ[n], {y[0] == 0, y[1] == 1, ϕ[0] == 0}}, 
 y[n], n
];

ListPlot[
  Transpose@Table[{y[n]} /. First[%],
  {n, 0, 350}], 
  Joined -> True, PlotRange -> All
]

I'd immensely appreciate any assistance.

added 30 characters in body
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george2079
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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_] = With[{k = 1.01}, JacobiAmplitude[k t, k^-3]]; Plot[[Phi][t], {t, 0, 50}]

\[Phi][t_] = 
With[{k = 1.01}, JacobiAmplitude[k t, k^-3]]; 
Plot[\[Phi][t], {t, 0, 50}]

I am using RSolve to solve a second-order difference equation and want to add a discrete-time version of the JacobiAmplitude function to the model as a forcing term.

I'd like to put a discrete-time JacobiAmplitude function, [Phi][n], into the following difference equation:

RSolve[{y[n + 2] - y[n + 1] + 0.99*y[n] == [Phi][n], {y[0] == 0, y[1] == 1, [Phi][0] == 0}}, y[n], n]; ListPlot[Transpose@Table[{y[n]} /. First[%], {n, 0, 350}], Joined -> True, PlotRange -> All]

RSolve[{y[n + 2] - y[n + 1] + 0.99*y[n] == \[Phi][n], {y[0] == 0, 
    y[1] == 1, \[Phi][0] == 0}}, y[n], n];
ListPlot[Transpose@Table[{y[n]} /. First[%], {n, 0, 350}], 
 Joined -> True, PlotRange -> All]

I'd immensely appreciate any assistance.

Thanks.

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_] = With[{k = 1.01}, JacobiAmplitude[k t, k^-3]]; Plot[[Phi][t], {t, 0, 50}]

I am using RSolve to solve a second-order difference equation and want to add a discrete-time version of the JacobiAmplitude function to the model as a forcing term.

I'd like to put a discrete-time JacobiAmplitude function, [Phi][n], into the following difference equation:

RSolve[{y[n + 2] - y[n + 1] + 0.99*y[n] == [Phi][n], {y[0] == 0, y[1] == 1, [Phi][0] == 0}}, y[n], n]; ListPlot[Transpose@Table[{y[n]} /. First[%], {n, 0, 350}], Joined -> True, PlotRange -> All]

I'd immensely appreciate any assistance.

Thanks.

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_] = 
With[{k = 1.01}, JacobiAmplitude[k t, k^-3]]; 
Plot[\[Phi][t], {t, 0, 50}]

I am using RSolve to solve a second-order difference equation and want to add a discrete-time version of the JacobiAmplitude function to the model as a forcing term.

I'd like to put a discrete-time JacobiAmplitude function, [Phi][n], into the following difference equation:

RSolve[{y[n + 2] - y[n + 1] + 0.99*y[n] == \[Phi][n], {y[0] == 0, 
    y[1] == 1, \[Phi][0] == 0}}, y[n], n];
ListPlot[Transpose@Table[{y[n]} /. First[%], {n, 0, 350}], 
 Joined -> True, PlotRange -> All]

I'd immensely appreciate any assistance.

Thanks.

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