Finding NDSolve method details
4
$begingroup$
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 Mar 24 at 4:14
xzczd
27.4k573255
asked Mar 24 at 1:09
sana alharbisana alharbi
456
$endgroup$
|
show 7 more comments
4
$begingroup$
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 Mar 24 at 4:14
xzczd
27.4k573255
asked Mar 24 at 1:09
sana alharbisana alharbi
456
$endgroup$
2
$begingroup$
Partial duplicate: mathematica.stackexchange.com/questions/145/…
$endgroup$
– Michael E2
Mar 24 at 1:17
1
$begingroup$
Another partial duplicate: mathematica.stackexchange.com/questions/102704/…
$endgroup$
– Michael E2
Mar 24 at 1:37
1
$begingroup$
You say you don't understand some technique or other, nor the output of yourTracecommand. 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
Mar 24 at 1:44
2
$begingroup$
"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
Mar 24 at 3:39
3
$begingroup$
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
Mar 24 at 3:59
|
show 7 more comments
4
4
4
0
$begingroup$
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 Mar 24 at 4:14
xzczd
27.4k573255
asked Mar 24 at 1:09
sana alharbisana alharbi
456
$endgroup$
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 Mar 24 at 4:14
xzczd
27.4k573255
asked Mar 24 at 1:09
sana alharbisana alharbi
456
edited Mar 24 at 4:14
xzczd
27.4k573255
asked Mar 24 at 1:09
sana alharbisana alharbi
456
edited Mar 24 at 4:14
xzczd
27.4k573255
edited Mar 24 at 4:14
xzczd
27.4k573255
edited Mar 24 at 4:14
xzczd
27.4k573255
27.4k573255
asked Mar 24 at 1:09
sana alharbisana alharbi
456
asked Mar 24 at 1:09
sana alharbisana alharbi
456
asked Mar 24 at 1:09
sana alharbisana alharbi
456
456
2
$begingroup$
Partial duplicate: mathematica.stackexchange.com/questions/145/…
$endgroup$
– Michael E2
Mar 24 at 1:17
1
$begingroup$
Another partial duplicate: mathematica.stackexchange.com/questions/102704/…
$endgroup$
– Michael E2
Mar 24 at 1:37
1
$begingroup$
You say you don't understand some technique or other, nor the output of yourTracecommand. 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
Mar 24 at 1:44
2
$begingroup$
"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
Mar 24 at 3:39
3
$begingroup$
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
Mar 24 at 3:59
|
show 7 more comments
2
$begingroup$
Partial duplicate: mathematica.stackexchange.com/questions/145/…
$endgroup$
– Michael E2
Mar 24 at 1:17
1
$begingroup$
Another partial duplicate: mathematica.stackexchange.com/questions/102704/…
$endgroup$
– Michael E2
Mar 24 at 1:37
1
$begingroup$
You say you don't understand some technique or other, nor the output of yourTracecommand. 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
Mar 24 at 1:44
2
$begingroup$
"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
Mar 24 at 3:39
3
$begingroup$
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
Mar 24 at 3:59
2
2
$begingroup$
Partial duplicate: mathematica.stackexchange.com/questions/145/…
$endgroup$
– Michael E2
Mar 24 at 1:17
$begingroup$
Partial duplicate: mathematica.stackexchange.com/questions/145/…
$endgroup$
– Michael E2
Mar 24 at 1:17
1
1
$begingroup$
Another partial duplicate: mathematica.stackexchange.com/questions/102704/…
$endgroup$
– Michael E2
Mar 24 at 1:37
$begingroup$
Another partial duplicate: mathematica.stackexchange.com/questions/102704/…
$endgroup$
– Michael E2
Mar 24 at 1:37
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
Mar 24 at 1:44
$begingroup$
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
Mar 24 at 1:44
2
2
$begingroup$
"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
Mar 24 at 3:39
$begingroup$
"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
Mar 24 at 3:39
3
3
$begingroup$
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
Mar 24 at 3:59
$begingroup$
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
Mar 24 at 3:59
|
show 7 more comments
1 Answer
1
active
oldest
votes
6
$begingroup$
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 Mar 24 at 5:09
zhkzhk
10.1k11533
$endgroup$
$begingroup$
Thank you so much @zhk but how can defend the axes for both figures? the first as x represented steps and y residual error. the second one x represents the t time and y residual error. sorry if my question is trivial but it is first time to see the code
$endgroup$
– sana alharbi
Mar 24 at 9:13
add a comment |
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
});
}
});
draft saved
draft discarded
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
6
$begingroup$
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 Mar 24 at 5:09
zhkzhk
10.1k11533
$endgroup$
$begingroup$
Thank you so much @zhk but how can defend the axes for both figures? the first as x represented steps and y residual error. the second one x represents the t time and y residual error. sorry if my question is trivial but it is first time to see the code
$endgroup$
– sana alharbi
Mar 24 at 9:13
add a comment |
6
$begingroup$
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 Mar 24 at 5:09
zhkzhk
10.1k11533
$endgroup$
$begingroup$
Thank you so much @zhk but how can defend the axes for both figures? the first as x represented steps and y residual error. the second one x represents the t time and y residual error. sorry if my question is trivial but it is first time to see the code
$endgroup$
– sana alharbi
Mar 24 at 9:13
add a comment |
6
6
6
$begingroup$
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 Mar 24 at 5:09
zhkzhk
10.1k11533
$endgroup$
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 Mar 24 at 5:09
zhkzhk
10.1k11533
answered Mar 24 at 5:09
zhkzhk
10.1k11533
answered Mar 24 at 5:09
zhkzhk
10.1k11533
answered Mar 24 at 5:09
zhkzhk
10.1k11533
10.1k11533
$begingroup$
Thank you so much @zhk but how can defend the axes for both figures? the first as x represented steps and y residual error. the second one x represents the t time and y residual error. sorry if my question is trivial but it is first time to see the code
$endgroup$
– sana alharbi
Mar 24 at 9:13
add a comment |
$begingroup$
Thank you so much @zhk but how can defend the axes for both figures? the first as x represented steps and y residual error. the second one x represents the t time and y residual error. sorry if my question is trivial but it is first time to see the code
$endgroup$
– sana alharbi
Mar 24 at 9:13
$begingroup$
Thank you so much @zhk but how can defend the axes for both figures? the first as x represented steps and y residual error. the second one x represents the t time and y residual error. sorry if my question is trivial but it is first time to see the code
$endgroup$
– sana alharbi
Mar 24 at 9:13
$begingroup$
Thank you so much @zhk but how can defend the axes for both figures? the first as x represented steps and y residual error. the second one x represents the t time and y residual error. sorry if my question is trivial but it is first time to see the code
$endgroup$
– sana alharbi
Mar 24 at 9:13
add a comment |
draft saved
draft discarded
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.
draft saved
draft discarded
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
Mar 24 at 1:17
1
$begingroup$
Another partial duplicate: mathematica.stackexchange.com/questions/102704/…
$endgroup$
– Michael E2
Mar 24 at 1:37
1
$begingroup$
You say you don't understand some technique or other, nor the output of your
Tracecommand. 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
Mar 24 at 1:44
2
$begingroup$
"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
Mar 24 at 3:39
3
$begingroup$
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
Mar 24 at 3:59