Going back in time in and initial value problemsolving coupled ODEs with initial-value and final-value constraintsOptimal ODE method for fixed number of RHS evaluations4th-order Runge-Kutta method for coupled harmonic oscillatorHow can I call the Boost C++ odeint Runge-Kutta integrator for a system of ODEs?Numerical solution of IVP for linear ODE with variable coefficient blows upObject falling with air resistance using Runge-KuttaODE System doesn't work when step size (h) is bigger than 1Prescribing variables as an excitation in Runge-Kutta methodAdam Bashforth 4 method: how to determine starting values and stil keep the the order of accuracyIs there any explicit symplectic Runge-Kutta method?
Non-misogynistic way to say “asshole”?
Can I enter the UK for 24 hours from a Schengen area, holding an Indian passport?
Encounter design and XP thresholds
Improve appearance of the table in Latex
Is there any proof that high saturation and contrast makes a picture more appealing in social media?
Greeting with "Ho"
What is the "ls" directory in my home directory?
Umlaut character order when sorting
Designing a magic-compatible polearm
Why is "Congress shall have power to enforce this article by appropriate legislation" necessary?
What does this Swiss black on yellow rectangular traffic sign with a symbol looking like a dart mean?
Are there any individual aliens that have gained superpowers in the Marvel universe?
"Correct me if I'm wrong"
What triggered jesuits' ban on infinitesimals in 1632?
What is "industrial ethernet"?
Methodology: Writing unit tests for another developer
Can the pre-order traversal of two different trees be the same even though they are different?
Covering index used despite missing column
How to work with PETG? Settings, caveats, etc
How hard is it to distinguish between remote access to a virtual machine vs a piece of hardware?
What is the oldest commercial MS-DOS program that can run on modern versions of Windows without third-party software?
Extending prime numbers digit by digit while retaining primality
Second 100 amp breaker inside existing 200 amp residential panel for new detached garage
Why don't countries like Japan just print more money?
Going back in time in and initial value problem
solving coupled ODEs with initial-value and final-value constraintsOptimal ODE method for fixed number of RHS evaluations4th-order Runge-Kutta method for coupled harmonic oscillatorHow can I call the Boost C++ odeint Runge-Kutta integrator for a system of ODEs?Numerical solution of IVP for linear ODE with variable coefficient blows upObject falling with air resistance using Runge-KuttaODE System doesn't work when step size (h) is bigger than 1Prescribing variables as an excitation in Runge-Kutta methodAdam Bashforth 4 method: how to determine starting values and stil keep the the order of accuracyIs there any explicit symplectic Runge-Kutta method?
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
Consider an initial value problem (IVP) $y'=f(t,y)$ with the initial value given by $y(t=0) = 0$.
If I need to find $y(t^*)$, hence finding the path for $y$ in $t in [0,t^*]$ and $t^*<0$; is the problem then still an initial value problem? In other words can you go back in time in IVP.
The reason I ask is that I have an algorithm where in each step I need to solve for different $t^*$. I intend to use solve_ivp in Python which is based on Runge-Kutta 45 method and I want to know if there are any theoretical contradictions when I apply RK45.
I know that if I will use Eulers method then there is no problem. But what about RK45. Will I get the desired result.
ode numerics
edited 7 hours ago
GertVdE
5,4301535
asked 8 hours ago
k.dkhkk.dkhk
1495
$endgroup$
add a comment |
$begingroup$
Consider an initial value problem (IVP) $y'=f(t,y)$ with the initial value given by $y(t=0) = 0$.
If I need to find $y(t^*)$, hence finding the path for $y$ in $t in [0,t^*]$ and $t^*<0$; is the problem then still an initial value problem? In other words can you go back in time in IVP.
The reason I ask is that I have an algorithm where in each step I need to solve for different $t^*$. I intend to use solve_ivp in Python which is based on Runge-Kutta 45 method and I want to know if there are any theoretical contradictions when I apply RK45.
I know that if I will use Eulers method then there is no problem. But what about RK45. Will I get the desired result.
ode numerics
edited 7 hours ago
GertVdE
5,4301535
asked 8 hours ago
k.dkhkk.dkhk
1495
$endgroup$
add a comment |
$begingroup$
Consider an initial value problem (IVP) $y'=f(t,y)$ with the initial value given by $y(t=0) = 0$.
If I need to find $y(t^*)$, hence finding the path for $y$ in $t in [0,t^*]$ and $t^*<0$; is the problem then still an initial value problem? In other words can you go back in time in IVP.
The reason I ask is that I have an algorithm where in each step I need to solve for different $t^*$. I intend to use solve_ivp in Python which is based on Runge-Kutta 45 method and I want to know if there are any theoretical contradictions when I apply RK45.
I know that if I will use Eulers method then there is no problem. But what about RK45. Will I get the desired result.
ode numerics
edited 7 hours ago
GertVdE
5,4301535
asked 8 hours ago
k.dkhkk.dkhk
1495
$endgroup$
Consider an initial value problem (IVP) $y'=f(t,y)$ with the initial value given by $y(t=0) = 0$.
If I need to find $y(t^*)$, hence finding the path for $y$ in $t in [0,t^*]$ and $t^*<0$; is the problem then still an initial value problem? In other words can you go back in time in IVP.
The reason I ask is that I have an algorithm where in each step I need to solve for different $t^*$. I intend to use solve_ivp in Python which is based on Runge-Kutta 45 method and I want to know if there are any theoretical contradictions when I apply RK45.
I know that if I will use Eulers method then there is no problem. But what about RK45. Will I get the desired result.
ode numerics
ode numerics
edited 7 hours ago
GertVdE
5,4301535
asked 8 hours ago
k.dkhkk.dkhk
1495
edited 7 hours ago
GertVdE
5,4301535
asked 8 hours ago
k.dkhkk.dkhk
1495
edited 7 hours ago
GertVdE
5,4301535
edited 7 hours ago
GertVdE
5,4301535
edited 7 hours ago
GertVdE
5,4301535
5,4301535
asked 8 hours ago
k.dkhkk.dkhk
1495
asked 8 hours ago
k.dkhkk.dkhk
1495
asked 8 hours ago
k.dkhkk.dkhk
1495
1495
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
This is technically still an IVP if you do an appropriate change of variables. Given your time is between $t in [t^*, 0]$, make a new time variable $tau = -t$ so that $tau in [0, -t^*]$ and you can modify the time derivatives accordingly. This means that you should have the differential equation $fracdydtau = -f(-tau, y)$ with $y(tau = 0) = 0$ as your new IVP. This implies that you should be able to use Runge-Kutta approaches just fine.
answered 6 hours ago
spektrspektr
2,4761913
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "363"
;
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%2fscicomp.stackexchange.com%2fquestions%2f32903%2fgoing-back-in-time-in-and-initial-value-problem%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
$begingroup$
This is technically still an IVP if you do an appropriate change of variables. Given your time is between $t in [t^*, 0]$, make a new time variable $tau = -t$ so that $tau in [0, -t^*]$ and you can modify the time derivatives accordingly. This means that you should have the differential equation $fracdydtau = -f(-tau, y)$ with $y(tau = 0) = 0$ as your new IVP. This implies that you should be able to use Runge-Kutta approaches just fine.
answered 6 hours ago
spektrspektr
2,4761913
$endgroup$
add a comment |
$begingroup$
This is technically still an IVP if you do an appropriate change of variables. Given your time is between $t in [t^*, 0]$, make a new time variable $tau = -t$ so that $tau in [0, -t^*]$ and you can modify the time derivatives accordingly. This means that you should have the differential equation $fracdydtau = -f(-tau, y)$ with $y(tau = 0) = 0$ as your new IVP. This implies that you should be able to use Runge-Kutta approaches just fine.
answered 6 hours ago
spektrspektr
2,4761913
$endgroup$
add a comment |
$begingroup$
This is technically still an IVP if you do an appropriate change of variables. Given your time is between $t in [t^*, 0]$, make a new time variable $tau = -t$ so that $tau in [0, -t^*]$ and you can modify the time derivatives accordingly. This means that you should have the differential equation $fracdydtau = -f(-tau, y)$ with $y(tau = 0) = 0$ as your new IVP. This implies that you should be able to use Runge-Kutta approaches just fine.
answered 6 hours ago
spektrspektr
2,4761913
$endgroup$
This is technically still an IVP if you do an appropriate change of variables. Given your time is between $t in [t^*, 0]$, make a new time variable $tau = -t$ so that $tau in [0, -t^*]$ and you can modify the time derivatives accordingly. This means that you should have the differential equation $fracdydtau = -f(-tau, y)$ with $y(tau = 0) = 0$ as your new IVP. This implies that you should be able to use Runge-Kutta approaches just fine.
answered 6 hours ago
spektrspektr
2,4761913
answered 6 hours ago
spektrspektr
2,4761913
answered 6 hours ago
spektrspektr
2,4761913
answered 6 hours ago
spektrspektr
2,4761913
2,4761913
add a comment |
add a comment |
Thanks for contributing an answer to Computational Science 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%2fscicomp.stackexchange.com%2fquestions%2f32903%2fgoing-back-in-time-in-and-initial-value-problem%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
