Finding NDSolve method detailsHow to find out which method Mathematica selected?inspecting step size and...
Approximating irrational number to rational number
Question about the proof of Second Isomorphism Theorem
Create all possible words using a set or letters
What should you do if you miss a job interview (deliberately)?
Why do we read the Megillah by night and by day?
Lowest total scrabble score
Problem with TransformedDistribution
Does a 'pending' US visa application constitute a denial?
Multiplicative persistence
Electoral considerations aside, what are potential benefits, for the US, of policy changes proposed by the tweet recognizing Golan annexation?
Does an advisor owe his/her student anything? Will an advisor keep a PhD student only out of pity?
Should I stop contributing to retirement accounts?
How much character growth crosses the line into breaking the character
What if a revenant (monster) gains fire resistance?
Start making guitar arrangements
Why does the Sun have different day lengths, but not the gas giants?
Is the U.S. Code copyrighted by the Government?
Can someone explain how this makes sense electrically?
What was the exact wording from Ivanhoe of this advice on how to free yourself from slavery?
Is there a single word describing earning money through any means?
Longest common substring in linear time
Fear of getting stuck on one programming language / technology that is not used in my country
Are the IPv6 address space and IPv4 address space completely disjoint?
When a Cleric spontaneously casts a Cure Light Wounds spell, will a Pearl of Power recover the original spell or Cure Light Wounds?
Finding NDSolve method details
How to find out which method Mathematica selected?inspecting step size and order of $tt NDSolve$What does MaxStepFraction do?How does Mathematica resolve symbolic systems of inequalities?NDSolve and strange “nonlinear coefficients problem”The idea behind Stiffness switching method with NDsolveProblems when solving a nonlinear PDE system with NDSolveSingularity treatment in a simple problemPDEs : automatic method choice : TensorProductGrid or FiniteElement?NDSolve struggling with tricky boundary conditionsNDSolve and memory usedDetails of NDSolve calling LSODA
$begingroup$
I have eqs about the NDSolve, I know this code given the solving automatically.
How can I find out what method is used behind the scenes? How can I gauge the reliability level, find how many iterations have been used, the order of method. How can I estimate the error?
I found hints on this site, but I still do not fully understand.
It is impossible to say NDSolve has automatically solution for publishing paper?
I used this code related to my system:
r = 0.431201; β = 2.99 *10^-6; σ = 0.7; δ = 0.57;
{m = 0.3, η = 0.1, μ = 0.1, ρ = 0.3};
S = {N1'[t] == r N1[t] (1 - β N1[t]) - η N1[t] I1[t],
I1'[t] == σ + (ρ N1[t] I1[t])/( m + N1[t]) - δ I1[t] - μ N1[t] I1[t]};
c = {N1[0] == 1, I1[0] == 1.22};
Select[Flatten[
Trace[
NDSolve[{S, c}, {N1, I1}, {t, 0, 30}],
TraceInternal -> True]],
!FreeQ[#, Method | NDSolve`MethodData] &]
but I don't understand the output.
differential-equations implementation-details
edited 2 hours ago
xzczd
27.4k573254
asked 5 hours ago
sana alharbisana alharbi
356
$endgroup$
|
show 5 more comments
$begingroup$
I have eqs about the NDSolve, I know this code given the solving automatically.
How can I find out what method is used behind the scenes? How can I gauge the reliability level, find how many iterations have been used, the order of method. How can I estimate the error?
I found hints on this site, but I still do not fully understand.
It is impossible to say NDSolve has automatically solution for publishing paper?
I used this code related to my system:
r = 0.431201; β = 2.99 *10^-6; σ = 0.7; δ = 0.57;
{m = 0.3, η = 0.1, μ = 0.1, ρ = 0.3};
S = {N1'[t] == r N1[t] (1 - β N1[t]) - η N1[t] I1[t],
I1'[t] == σ + (ρ N1[t] I1[t])/( m + N1[t]) - δ I1[t] - μ N1[t] I1[t]};
c = {N1[0] == 1, I1[0] == 1.22};
Select[Flatten[
Trace[
NDSolve[{S, c}, {N1, I1}, {t, 0, 30}],
TraceInternal -> True]],
!FreeQ[#, Method | NDSolve`MethodData] &]
but I don't understand the output.
differential-equations implementation-details
edited 2 hours ago
xzczd
27.4k573254
asked 5 hours ago
sana alharbisana alharbi
356
$endgroup$
2
$begingroup$
Partial duplicate: mathematica.stackexchange.com/questions/145/…
$endgroup$
– Michael E2
5 hours ago
1
$begingroup$
Another partial duplicate: mathematica.stackexchange.com/questions/102704/…
$endgroup$
– Michael E2
5 hours ago
1
$begingroup$
You say you don't understand some technique or other, nor the output of yourTrace[]command. But the first is a very general statement about things already explained and the second is about a command that no one else can reproduce
$endgroup$
– Michael E2
5 hours ago
1
$begingroup$
"It is impossible to say NDSolve has automatically solution for publishing paper. " Simply saying "I've usedNDSolvefunction of software Mathematica" is enough in many cases, AFAIK.
$endgroup$
– xzczd
3 hours ago
2
$begingroup$
Well, if the reviewer insists on such stuff, given that your system isn't that difficult, a possible workaround at this point is to choose a primary method like classical RK4 to solve the problem. The way to choose classical RK4 inNDSolvecan be found intutorial/NDSolveExplicitRungeKutta#1456351317, then you just need to setMethod -> {"ExplicitRungeKutta", "DifferenceOrder" -> 4, "Coefficients" -> ClassicalRungeKuttaCoefficients}, StartingStepSize -> 1/20000, MaxSteps -> InfinityinNDSolve. The solving process is slower but gives the same result as given by default.
$endgroup$
– xzczd
2 hours ago
|
show 5 more comments
$begingroup$
I have eqs about the NDSolve, I know this code given the solving automatically.
How can I find out what method is used behind the scenes? How can I gauge the reliability level, find how many iterations have been used, the order of method. How can I estimate the error?
I found hints on this site, but I still do not fully understand.
It is impossible to say NDSolve has automatically solution for publishing paper?
I used this code related to my system:
r = 0.431201; β = 2.99 *10^-6; σ = 0.7; δ = 0.57;
{m = 0.3, η = 0.1, μ = 0.1, ρ = 0.3};
S = {N1'[t] == r N1[t] (1 - β N1[t]) - η N1[t] I1[t],
I1'[t] == σ + (ρ N1[t] I1[t])/( m + N1[t]) - δ I1[t] - μ N1[t] I1[t]};
c = {N1[0] == 1, I1[0] == 1.22};
Select[Flatten[
Trace[
NDSolve[{S, c}, {N1, I1}, {t, 0, 30}],
TraceInternal -> True]],
!FreeQ[#, Method | NDSolve`MethodData] &]
but I don't understand the output.
differential-equations implementation-details
edited 2 hours ago
xzczd
27.4k573254
asked 5 hours ago
sana alharbisana alharbi
356
$endgroup$
I have eqs about the NDSolve, I know this code given the solving automatically.
How can I find out what method is used behind the scenes? How can I gauge the reliability level, find how many iterations have been used, the order of method. How can I estimate the error?
I found hints on this site, but I still do not fully understand.
It is impossible to say NDSolve has automatically solution for publishing paper?
I used this code related to my system:
r = 0.431201; β = 2.99 *10^-6; σ = 0.7; δ = 0.57;
{m = 0.3, η = 0.1, μ = 0.1, ρ = 0.3};
S = {N1'[t] == r N1[t] (1 - β N1[t]) - η N1[t] I1[t],
I1'[t] == σ + (ρ N1[t] I1[t])/( m + N1[t]) - δ I1[t] - μ N1[t] I1[t]};
c = {N1[0] == 1, I1[0] == 1.22};
Select[Flatten[
Trace[
NDSolve[{S, c}, {N1, I1}, {t, 0, 30}],
TraceInternal -> True]],
!FreeQ[#, Method | NDSolve`MethodData] &]
but I don't understand the output.
differential-equations implementation-details
differential-equations implementation-details
edited 2 hours ago
xzczd
27.4k573254
asked 5 hours ago
sana alharbisana alharbi
356
edited 2 hours ago
xzczd
27.4k573254
asked 5 hours ago
sana alharbisana alharbi
356
edited 2 hours ago
xzczd
27.4k573254
edited 2 hours ago
xzczd
27.4k573254
edited 2 hours ago
xzczd
27.4k573254
27.4k573254
asked 5 hours ago
sana alharbisana alharbi
356
asked 5 hours ago
sana alharbisana alharbi
356
asked 5 hours ago
sana alharbisana alharbi
356
356
2
$begingroup$
Partial duplicate: mathematica.stackexchange.com/questions/145/…
$endgroup$
– Michael E2
5 hours ago
1
$begingroup$
Another partial duplicate: mathematica.stackexchange.com/questions/102704/…
$endgroup$
– Michael E2
5 hours ago
1
$begingroup$
You say you don't understand some technique or other, nor the output of yourTrace[]command. But the first is a very general statement about things already explained and the second is about a command that no one else can reproduce
$endgroup$
– Michael E2
5 hours ago
1
$begingroup$
"It is impossible to say NDSolve has automatically solution for publishing paper. " Simply saying "I've usedNDSolvefunction of software Mathematica" is enough in many cases, AFAIK.
$endgroup$
– xzczd
3 hours ago
2
$begingroup$
Well, if the reviewer insists on such stuff, given that your system isn't that difficult, a possible workaround at this point is to choose a primary method like classical RK4 to solve the problem. The way to choose classical RK4 inNDSolvecan be found intutorial/NDSolveExplicitRungeKutta#1456351317, then you just need to setMethod -> {"ExplicitRungeKutta", "DifferenceOrder" -> 4, "Coefficients" -> ClassicalRungeKuttaCoefficients}, StartingStepSize -> 1/20000, MaxSteps -> InfinityinNDSolve. The solving process is slower but gives the same result as given by default.
$endgroup$
– xzczd
2 hours ago
|
show 5 more comments
2
$begingroup$
Partial duplicate: mathematica.stackexchange.com/questions/145/…
$endgroup$
– Michael E2
5 hours ago
1
$begingroup$
Another partial duplicate: mathematica.stackexchange.com/questions/102704/…
$endgroup$
– Michael E2
5 hours ago
1
$begingroup$
You say you don't understand some technique or other, nor the output of yourTrace[]command. But the first is a very general statement about things already explained and the second is about a command that no one else can reproduce
$endgroup$
– Michael E2
5 hours ago
1
$begingroup$
"It is impossible to say NDSolve has automatically solution for publishing paper. " Simply saying "I've usedNDSolvefunction of software Mathematica" is enough in many cases, AFAIK.
$endgroup$
– xzczd
3 hours ago
2
$begingroup$
Well, if the reviewer insists on such stuff, given that your system isn't that difficult, a possible workaround at this point is to choose a primary method like classical RK4 to solve the problem. The way to choose classical RK4 inNDSolvecan be found intutorial/NDSolveExplicitRungeKutta#1456351317, then you just need to setMethod -> {"ExplicitRungeKutta", "DifferenceOrder" -> 4, "Coefficients" -> ClassicalRungeKuttaCoefficients}, StartingStepSize -> 1/20000, MaxSteps -> InfinityinNDSolve. The solving process is slower but gives the same result as given by default.
$endgroup$
– xzczd
2 hours ago
2
2
$begingroup$
Partial duplicate: mathematica.stackexchange.com/questions/145/…
$endgroup$
– Michael E2
5 hours ago
$begingroup$
Partial duplicate: mathematica.stackexchange.com/questions/145/…
$endgroup$
– Michael E2
5 hours ago
1
1
$begingroup$
Another partial duplicate: mathematica.stackexchange.com/questions/102704/…
$endgroup$
– Michael E2
5 hours ago
$begingroup$
Another partial duplicate: mathematica.stackexchange.com/questions/102704/…
$endgroup$
– Michael E2
5 hours ago
1
1
$begingroup$
You say you don't understand some technique or other, nor the output of your
Trace[] command. But the first is a very general statement about things already explained and the second is about a command that no one else can reproduce$endgroup$
– Michael E2
5 hours ago
$begingroup$
You say you don't understand some technique or other, nor the output of your
Trace[] command. But the first is a very general statement about things already explained and the second is about a command that no one else can reproduce$endgroup$
– Michael E2
5 hours ago
1
1
$begingroup$
"It is impossible to say NDSolve has automatically solution for publishing paper. " Simply saying "I've used
NDSolve function of software Mathematica" is enough in many cases, AFAIK.$endgroup$
– xzczd
3 hours ago
$begingroup$
"It is impossible to say NDSolve has automatically solution for publishing paper. " Simply saying "I've used
NDSolve function of software Mathematica" is enough in many cases, AFAIK.$endgroup$
– xzczd
3 hours ago
2
2
$begingroup$
Well, if the reviewer insists on such stuff, given that your system isn't that difficult, a possible workaround at this point is to choose a primary method like classical RK4 to solve the problem. The way to choose classical RK4 in
NDSolve can be found in tutorial/NDSolveExplicitRungeKutta#1456351317, then you just need to set Method -> {"ExplicitRungeKutta", "DifferenceOrder" -> 4, "Coefficients" -> ClassicalRungeKuttaCoefficients}, StartingStepSize -> 1/20000, MaxSteps -> Infinity in NDSolve. The solving process is slower but gives the same result as given by default.$endgroup$
– xzczd
2 hours ago
$begingroup$
Well, if the reviewer insists on such stuff, given that your system isn't that difficult, a possible workaround at this point is to choose a primary method like classical RK4 to solve the problem. The way to choose classical RK4 in
NDSolve can be found in tutorial/NDSolveExplicitRungeKutta#1456351317, then you just need to set Method -> {"ExplicitRungeKutta", "DifferenceOrder" -> 4, "Coefficients" -> ClassicalRungeKuttaCoefficients}, StartingStepSize -> 1/20000, MaxSteps -> Infinity in NDSolve. The solving process is slower but gives the same result as given by default.$endgroup$
– xzczd
2 hours ago
|
show 5 more comments
1 Answer
1
active
oldest
votes
$begingroup$
Comment
In response to your question, you already got very valuable comments. I will just try to comment on
How can I estimate the error?
For this I am going to plot residual error at steps and time, which will show the reliability and accuracy of NDSolve,
r = 0.431201; [Beta] = 2.99*10^-6; [Sigma] = 0.7; [Delta] = 0.57;
m = 0.3; [Eta] = 0.1; [Mu] = 0.1; [Rho] = 0.3;
ode = {N1'[t] == r N1[t] (1 - [Beta] N1[t]) - [Eta] N1[t] I1[t],
I1'[t] == [Sigma] + ([Rho] N1[t] I1[t])/(m + N1[t]) - [Delta] I1[t] - [Mu] N1[t] I1[t]};
bcs = {N1[0] == 1, I1[0] == 1.22};
residuals = ode /. Equal -> Subtract;
{s} = NDSolve[{ode, bcs}, {N1, I1}, {t, 20}, InterpolationOrder -> All];
N1["Coordinates"] /. s;
residuals /. t -> N1["Coordinates"] /. s;
ListPlot[Abs[Flatten /@ (residuals /. t -> N1["Coordinates"] /. s)], Frame -> True]
With[{data = {Table[{t, Abs@residuals[[1]]} /. s, {t, N1["Coordinates"] /. s // Flatten}]}},
ListLogPlot[data, Frame -> True, PlotRange -> All]]
Note: I adopted the above from this website but unable to find the link.
answered 1 hour ago
zhkzhk
10k11433
$endgroup$
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%2f193858%2ffinding-ndsolve-method-details%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
$begingroup$
Comment
In response to your question, you already got very valuable comments. I will just try to comment on
How can I estimate the error?
For this I am going to plot residual error at steps and time, which will show the reliability and accuracy of NDSolve,
r = 0.431201; [Beta] = 2.99*10^-6; [Sigma] = 0.7; [Delta] = 0.57;
m = 0.3; [Eta] = 0.1; [Mu] = 0.1; [Rho] = 0.3;
ode = {N1'[t] == r N1[t] (1 - [Beta] N1[t]) - [Eta] N1[t] I1[t],
I1'[t] == [Sigma] + ([Rho] N1[t] I1[t])/(m + N1[t]) - [Delta] I1[t] - [Mu] N1[t] I1[t]};
bcs = {N1[0] == 1, I1[0] == 1.22};
residuals = ode /. Equal -> Subtract;
{s} = NDSolve[{ode, bcs}, {N1, I1}, {t, 20}, InterpolationOrder -> All];
N1["Coordinates"] /. s;
residuals /. t -> N1["Coordinates"] /. s;
ListPlot[Abs[Flatten /@ (residuals /. t -> N1["Coordinates"] /. s)], Frame -> True]
With[{data = {Table[{t, Abs@residuals[[1]]} /. s, {t, N1["Coordinates"] /. s // Flatten}]}},
ListLogPlot[data, Frame -> True, PlotRange -> All]]
Note: I adopted the above from this website but unable to find the link.
answered 1 hour ago
zhkzhk
10k11433
$endgroup$
add a comment |
$begingroup$
Comment
In response to your question, you already got very valuable comments. I will just try to comment on
How can I estimate the error?
For this I am going to plot residual error at steps and time, which will show the reliability and accuracy of NDSolve,
r = 0.431201; [Beta] = 2.99*10^-6; [Sigma] = 0.7; [Delta] = 0.57;
m = 0.3; [Eta] = 0.1; [Mu] = 0.1; [Rho] = 0.3;
ode = {N1'[t] == r N1[t] (1 - [Beta] N1[t]) - [Eta] N1[t] I1[t],
I1'[t] == [Sigma] + ([Rho] N1[t] I1[t])/(m + N1[t]) - [Delta] I1[t] - [Mu] N1[t] I1[t]};
bcs = {N1[0] == 1, I1[0] == 1.22};
residuals = ode /. Equal -> Subtract;
{s} = NDSolve[{ode, bcs}, {N1, I1}, {t, 20}, InterpolationOrder -> All];
N1["Coordinates"] /. s;
residuals /. t -> N1["Coordinates"] /. s;
ListPlot[Abs[Flatten /@ (residuals /. t -> N1["Coordinates"] /. s)], Frame -> True]
With[{data = {Table[{t, Abs@residuals[[1]]} /. s, {t, N1["Coordinates"] /. s // Flatten}]}},
ListLogPlot[data, Frame -> True, PlotRange -> All]]
Note: I adopted the above from this website but unable to find the link.
answered 1 hour ago
zhkzhk
10k11433
$endgroup$
add a comment |
$begingroup$
Comment
In response to your question, you already got very valuable comments. I will just try to comment on
How can I estimate the error?
For this I am going to plot residual error at steps and time, which will show the reliability and accuracy of NDSolve,
r = 0.431201; [Beta] = 2.99*10^-6; [Sigma] = 0.7; [Delta] = 0.57;
m = 0.3; [Eta] = 0.1; [Mu] = 0.1; [Rho] = 0.3;
ode = {N1'[t] == r N1[t] (1 - [Beta] N1[t]) - [Eta] N1[t] I1[t],
I1'[t] == [Sigma] + ([Rho] N1[t] I1[t])/(m + N1[t]) - [Delta] I1[t] - [Mu] N1[t] I1[t]};
bcs = {N1[0] == 1, I1[0] == 1.22};
residuals = ode /. Equal -> Subtract;
{s} = NDSolve[{ode, bcs}, {N1, I1}, {t, 20}, InterpolationOrder -> All];
N1["Coordinates"] /. s;
residuals /. t -> N1["Coordinates"] /. s;
ListPlot[Abs[Flatten /@ (residuals /. t -> N1["Coordinates"] /. s)], Frame -> True]
With[{data = {Table[{t, Abs@residuals[[1]]} /. s, {t, N1["Coordinates"] /. s // Flatten}]}},
ListLogPlot[data, Frame -> True, PlotRange -> All]]
Note: I adopted the above from this website but unable to find the link.
answered 1 hour ago
zhkzhk
10k11433
$endgroup$
Comment
In response to your question, you already got very valuable comments. I will just try to comment on
How can I estimate the error?
For this I am going to plot residual error at steps and time, which will show the reliability and accuracy of NDSolve,
r = 0.431201; [Beta] = 2.99*10^-6; [Sigma] = 0.7; [Delta] = 0.57;
m = 0.3; [Eta] = 0.1; [Mu] = 0.1; [Rho] = 0.3;
ode = {N1'[t] == r N1[t] (1 - [Beta] N1[t]) - [Eta] N1[t] I1[t],
I1'[t] == [Sigma] + ([Rho] N1[t] I1[t])/(m + N1[t]) - [Delta] I1[t] - [Mu] N1[t] I1[t]};
bcs = {N1[0] == 1, I1[0] == 1.22};
residuals = ode /. Equal -> Subtract;
{s} = NDSolve[{ode, bcs}, {N1, I1}, {t, 20}, InterpolationOrder -> All];
N1["Coordinates"] /. s;
residuals /. t -> N1["Coordinates"] /. s;
ListPlot[Abs[Flatten /@ (residuals /. t -> N1["Coordinates"] /. s)], Frame -> True]
With[{data = {Table[{t, Abs@residuals[[1]]} /. s, {t, N1["Coordinates"] /. s // Flatten}]}},
ListLogPlot[data, Frame -> True, PlotRange -> All]]
Note: I adopted the above from this website but unable to find the link.
answered 1 hour ago
zhkzhk
10k11433
answered 1 hour ago
zhkzhk
10k11433
answered 1 hour ago
zhkzhk
10k11433
answered 1 hour ago
zhkzhk
10k11433
10k11433
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%2f193858%2ffinding-ndsolve-method-details%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
2
$begingroup$
Partial duplicate: mathematica.stackexchange.com/questions/145/…
$endgroup$
– Michael E2
5 hours ago
1
$begingroup$
Another partial duplicate: mathematica.stackexchange.com/questions/102704/…
$endgroup$
– Michael E2
5 hours ago
1
$begingroup$
You say you don't understand some technique or other, nor the output of your
Trace[]command. But the first is a very general statement about things already explained and the second is about a command that no one else can reproduce$endgroup$
– Michael E2
5 hours ago
1
$begingroup$
"It is impossible to say NDSolve has automatically solution for publishing paper. " Simply saying "I've used
NDSolvefunction of software Mathematica" is enough in many cases, AFAIK.$endgroup$
– xzczd
3 hours ago
2
$begingroup$
Well, if the reviewer insists on such stuff, given that your system isn't that difficult, a possible workaround at this point is to choose a primary method like classical RK4 to solve the problem. The way to choose classical RK4 in
NDSolvecan be found intutorial/NDSolveExplicitRungeKutta#1456351317, then you just need to setMethod -> {"ExplicitRungeKutta", "DifferenceOrder" -> 4, "Coefficients" -> ClassicalRungeKuttaCoefficients}, StartingStepSize -> 1/20000, MaxSteps -> InfinityinNDSolve. The solving process is slower but gives the same result as given by default.$endgroup$
– xzczd
2 hours ago