How to increase accuracy of Plot
$begingroup$
I have the following code below:
num = 25;
U[x_] := 50*(Sech[1.5*(x - 5.8)])^4 - 0.14*(Sech[0.5*(x - 6.5)])^2
V[x_] := U[x] - U[3.8]
Plot[V[x], {x, 0, 4.75}, PlotRange -> All];
A := 1.05459^2*0.01/2/1.6726/1.60219
{vals, funs} =
NDEigensystem[-(A/x)*D[x*D[[Psi][x], {x}], {x}] +
V[x]*[Psi][x], [Psi][x], {x, 0, 5}, num];
And I get next graphic:
Here, as I expect there should not be such a sharp peak at the beginning of Plot. So I tried to increase a number of points for Plot:
Plot[Evaluate[funs[[25]]/
Sqrt[NIntegrate[x*(funs[[25]])^2, {x, 0, 5},
AccuracyGoal -> 10]]], {x, 0, 5}, PlotLegends -> vals[[25]],
PlotRange -> All]
And get next:
It's the same graph but in different ranges. So my question is How can I do the same but in range from 0 to 5.
plotting graphics recursion precision-and-accuracy
asked 2 hours ago
JohnJohn
32716
$endgroup$
add a comment |
$begingroup$
I have the following code below:
num = 25;
U[x_] := 50*(Sech[1.5*(x - 5.8)])^4 - 0.14*(Sech[0.5*(x - 6.5)])^2
V[x_] := U[x] - U[3.8]
Plot[V[x], {x, 0, 4.75}, PlotRange -> All];
A := 1.05459^2*0.01/2/1.6726/1.60219
{vals, funs} =
NDEigensystem[-(A/x)*D[x*D[[Psi][x], {x}], {x}] +
V[x]*[Psi][x], [Psi][x], {x, 0, 5}, num];
And I get next graphic:
Here, as I expect there should not be such a sharp peak at the beginning of Plot. So I tried to increase a number of points for Plot:
Plot[Evaluate[funs[[25]]/
Sqrt[NIntegrate[x*(funs[[25]])^2, {x, 0, 5},
AccuracyGoal -> 10]]], {x, 0, 5}, PlotLegends -> vals[[25]],
PlotRange -> All]
And get next:
It's the same graph but in different ranges. So my question is How can I do the same but in range from 0 to 5.
plotting graphics recursion precision-and-accuracy
asked 2 hours ago
JohnJohn
32716
$endgroup$
$begingroup$
I think PlotPoints is the option you need
$endgroup$
– mikado
2 hours ago
1
$begingroup$
This is not an issue ofPlot. The interpolating function that you are using (funs[[25]]) already has this shape.
$endgroup$
– Sjoerd C. de Vries
2 hours ago
add a comment |
$begingroup$
I have the following code below:
num = 25;
U[x_] := 50*(Sech[1.5*(x - 5.8)])^4 - 0.14*(Sech[0.5*(x - 6.5)])^2
V[x_] := U[x] - U[3.8]
Plot[V[x], {x, 0, 4.75}, PlotRange -> All];
A := 1.05459^2*0.01/2/1.6726/1.60219
{vals, funs} =
NDEigensystem[-(A/x)*D[x*D[[Psi][x], {x}], {x}] +
V[x]*[Psi][x], [Psi][x], {x, 0, 5}, num];
And I get next graphic:
Here, as I expect there should not be such a sharp peak at the beginning of Plot. So I tried to increase a number of points for Plot:
Plot[Evaluate[funs[[25]]/
Sqrt[NIntegrate[x*(funs[[25]])^2, {x, 0, 5},
AccuracyGoal -> 10]]], {x, 0, 5}, PlotLegends -> vals[[25]],
PlotRange -> All]
And get next:
It's the same graph but in different ranges. So my question is How can I do the same but in range from 0 to 5.
plotting graphics recursion precision-and-accuracy
asked 2 hours ago
JohnJohn
32716
$endgroup$
I have the following code below:
num = 25;
U[x_] := 50*(Sech[1.5*(x - 5.8)])^4 - 0.14*(Sech[0.5*(x - 6.5)])^2
V[x_] := U[x] - U[3.8]
Plot[V[x], {x, 0, 4.75}, PlotRange -> All];
A := 1.05459^2*0.01/2/1.6726/1.60219
{vals, funs} =
NDEigensystem[-(A/x)*D[x*D[[Psi][x], {x}], {x}] +
V[x]*[Psi][x], [Psi][x], {x, 0, 5}, num];
And I get next graphic:
Here, as I expect there should not be such a sharp peak at the beginning of Plot. So I tried to increase a number of points for Plot:
Plot[Evaluate[funs[[25]]/
Sqrt[NIntegrate[x*(funs[[25]])^2, {x, 0, 5},
AccuracyGoal -> 10]]], {x, 0, 5}, PlotLegends -> vals[[25]],
PlotRange -> All]
And get next:
It's the same graph but in different ranges. So my question is How can I do the same but in range from 0 to 5.
plotting graphics recursion precision-and-accuracy
plotting graphics recursion precision-and-accuracy
asked 2 hours ago
JohnJohn
32716
asked 2 hours ago
JohnJohn
32716
asked 2 hours ago
JohnJohn
32716
asked 2 hours ago
JohnJohn
32716
asked 2 hours ago
JohnJohn
32716
32716
$begingroup$
I think PlotPoints is the option you need
$endgroup$
– mikado
2 hours ago
1
$begingroup$
This is not an issue ofPlot. The interpolating function that you are using (funs[[25]]) already has this shape.
$endgroup$
– Sjoerd C. de Vries
2 hours ago
add a comment |
$begingroup$
I think PlotPoints is the option you need
$endgroup$
– mikado
2 hours ago
1
$begingroup$
This is not an issue ofPlot. The interpolating function that you are using (funs[[25]]) already has this shape.
$endgroup$
– Sjoerd C. de Vries
2 hours ago
$begingroup$
I think PlotPoints is the option you need
$endgroup$
– mikado
2 hours ago
$begingroup$
I think PlotPoints is the option you need
$endgroup$
– mikado
2 hours ago
1
1
$begingroup$
This is not an issue of
Plot. The interpolating function that you are using (funs[[25]]) already has this shape.$endgroup$
– Sjoerd C. de Vries
2 hours ago
$begingroup$
This is not an issue of
Plot. The interpolating function that you are using (funs[[25]]) already has this shape.$endgroup$
– Sjoerd C. de Vries
2 hours ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The problem does not seem to be in Plot but in NDEigensystem. Apparently, the default method used for your function is not ideal. If you provide a method explicitly it seems to work better.
{vals, funs} =
NDEigensystem[
-(A/x)*D[x*D[ψ[x], {x}], {x}] + V[x]*ψ[x],
ψ[x],
{x, 0, 5},
num,
Method -> {"PDEDiscretization" ->
{"FiniteElement", {"MeshOptions" -> {"MaxCellMeasure" -> 0.001}}}}];
Multicolumn[Plot[#, {x, 0, 5}, PlotRange -> All] & /@ funs]
answered 1 hour ago
Sjoerd C. de VriesSjoerd C. de Vries
57.6k10155298
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The problem does not seem to be in Plot but in NDEigensystem. Apparently, the default method used for your function is not ideal. If you provide a method explicitly it seems to work better.
{vals, funs} =
NDEigensystem[
-(A/x)*D[x*D[ψ[x], {x}], {x}] + V[x]*ψ[x],
ψ[x],
{x, 0, 5},
num,
Method -> {"PDEDiscretization" ->
{"FiniteElement", {"MeshOptions" -> {"MaxCellMeasure" -> 0.001}}}}];
Multicolumn[Plot[#, {x, 0, 5}, PlotRange -> All] & /@ funs]
answered 1 hour ago
Sjoerd C. de VriesSjoerd C. de Vries
57.6k10155298
$endgroup$
add a comment |
$begingroup$
The problem does not seem to be in Plot but in NDEigensystem. Apparently, the default method used for your function is not ideal. If you provide a method explicitly it seems to work better.
{vals, funs} =
NDEigensystem[
-(A/x)*D[x*D[ψ[x], {x}], {x}] + V[x]*ψ[x],
ψ[x],
{x, 0, 5},
num,
Method -> {"PDEDiscretization" ->
{"FiniteElement", {"MeshOptions" -> {"MaxCellMeasure" -> 0.001}}}}];
Multicolumn[Plot[#, {x, 0, 5}, PlotRange -> All] & /@ funs]
answered 1 hour ago
Sjoerd C. de VriesSjoerd C. de Vries
57.6k10155298
$endgroup$
add a comment |
$begingroup$
The problem does not seem to be in Plot but in NDEigensystem. Apparently, the default method used for your function is not ideal. If you provide a method explicitly it seems to work better.
{vals, funs} =
NDEigensystem[
-(A/x)*D[x*D[ψ[x], {x}], {x}] + V[x]*ψ[x],
ψ[x],
{x, 0, 5},
num,
Method -> {"PDEDiscretization" ->
{"FiniteElement", {"MeshOptions" -> {"MaxCellMeasure" -> 0.001}}}}];
Multicolumn[Plot[#, {x, 0, 5}, PlotRange -> All] & /@ funs]
answered 1 hour ago
Sjoerd C. de VriesSjoerd C. de Vries
57.6k10155298
$endgroup$
The problem does not seem to be in Plot but in NDEigensystem. Apparently, the default method used for your function is not ideal. If you provide a method explicitly it seems to work better.
{vals, funs} =
NDEigensystem[
-(A/x)*D[x*D[ψ[x], {x}], {x}] + V[x]*ψ[x],
ψ[x],
{x, 0, 5},
num,
Method -> {"PDEDiscretization" ->
{"FiniteElement", {"MeshOptions" -> {"MaxCellMeasure" -> 0.001}}}}];
Multicolumn[Plot[#, {x, 0, 5}, PlotRange -> All] & /@ funs]
answered 1 hour ago
Sjoerd C. de VriesSjoerd C. de Vries
57.6k10155298
answered 1 hour ago
Sjoerd C. de VriesSjoerd C. de Vries
57.6k10155298
answered 1 hour ago
Sjoerd C. de VriesSjoerd C. de Vries
57.6k10155298
answered 1 hour ago
Sjoerd C. de VriesSjoerd C. de Vries
57.6k10155298
57.6k10155298
add a comment |
add a comment |
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$begingroup$
I think PlotPoints is the option you need
$endgroup$
– mikado
2 hours ago
1
$begingroup$
This is not an issue of
Plot. The interpolating function that you are using (funs[[25]]) already has this shape.$endgroup$
– Sjoerd C. de Vries
2 hours ago