How to increase the accuracy of a 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 the following graphic:
Here, as I expect there should not be such a sharp peak at the beginning of the plot. So I tried to increase a number of points for the 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 the following:
It's the same graph, but in different ranges. How can I do the same, but in range from 0 to 5?
plotting graphics recursion precision-and-accuracy
edited Mar 9 at 16:39
Peter Mortensen
33427
asked Mar 9 at 12:56
JohnJohn
33716
$endgroup$
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 the following graphic:
Here, as I expect there should not be such a sharp peak at the beginning of the plot. So I tried to increase a number of points for the 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 the following:
It's the same graph, but in different ranges. How can I do the same, but in range from 0 to 5?
plotting graphics recursion precision-and-accuracy
edited Mar 9 at 16:39
Peter Mortensen
33427
asked Mar 9 at 12:56
JohnJohn
33716
$endgroup$
$begingroup$
I think PlotPoints is the option you need
$endgroup$
– mikado
Mar 9 at 13:19
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
Mar 9 at 13:26
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 the following graphic:
Here, as I expect there should not be such a sharp peak at the beginning of the plot. So I tried to increase a number of points for the 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 the following:
It's the same graph, but in different ranges. How can I do the same, but in range from 0 to 5?
plotting graphics recursion precision-and-accuracy
edited Mar 9 at 16:39
Peter Mortensen
33427
asked Mar 9 at 12:56
JohnJohn
33716
$endgroup$
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 the following graphic:
Here, as I expect there should not be such a sharp peak at the beginning of the plot. So I tried to increase a number of points for the 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 the following:
It's the same graph, but in different ranges. 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
edited Mar 9 at 16:39
Peter Mortensen
33427
asked Mar 9 at 12:56
JohnJohn
33716
edited Mar 9 at 16:39
Peter Mortensen
33427
asked Mar 9 at 12:56
JohnJohn
33716
edited Mar 9 at 16:39
Peter Mortensen
33427
edited Mar 9 at 16:39
Peter Mortensen
33427
edited Mar 9 at 16:39
Peter Mortensen
33427
33427
asked Mar 9 at 12:56
JohnJohn
33716
asked Mar 9 at 12:56
JohnJohn
33716
asked Mar 9 at 12:56
JohnJohn
33716
33716
$begingroup$
I think PlotPoints is the option you need
$endgroup$
– mikado
Mar 9 at 13:19
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
Mar 9 at 13:26
add a comment |
$begingroup$
I think PlotPoints is the option you need
$endgroup$
– mikado
Mar 9 at 13:19
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
Mar 9 at 13:26
$begingroup$
I think PlotPoints is the option you need
$endgroup$
– mikado
Mar 9 at 13:19
$begingroup$
I think PlotPoints is the option you need
$endgroup$
– mikado
Mar 9 at 13:19
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
Mar 9 at 13:26
$begingroup$
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
Mar 9 at 13:26
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 Mar 9 at 13:48
Sjoerd C. de VriesSjoerd C. de Vries
57.7k10155298
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "387"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f192936%2fhow-to-increase-the-accuracy-of-a-plot%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
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 Mar 9 at 13:48
Sjoerd C. de VriesSjoerd C. de Vries
57.7k10155298
$endgroup$
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 Mar 9 at 13:48
Sjoerd C. de VriesSjoerd C. de Vries
57.7k10155298
$endgroup$
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 Mar 9 at 13:48
Sjoerd C. de VriesSjoerd C. de Vries
57.7k10155298
$endgroup$
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 Mar 9 at 13:48
Sjoerd C. de VriesSjoerd C. de Vries
57.7k10155298
answered Mar 9 at 13:48
Sjoerd C. de VriesSjoerd C. de Vries
57.7k10155298
answered Mar 9 at 13:48
Sjoerd C. de VriesSjoerd C. de Vries
57.7k10155298
answered Mar 9 at 13:48
Sjoerd C. de VriesSjoerd C. de Vries
57.7k10155298
57.7k10155298
add a comment |
add a comment |
Thanks for contributing an answer to Mathematica Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f192936%2fhow-to-increase-the-accuracy-of-a-plot%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
I think PlotPoints is the option you need
$endgroup$
– mikado
Mar 9 at 13:19
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
Mar 9 at 13:26