Plotting a solution of a differential equation with Sagemath
I need to solve a differential equation. The solution will depend on t and q, and I need to define that q piecewise depending on t.
var('k,Tmax,Tmin,w,T0,q'); T=function('T')(t); Te=function('Te')(t);
assume(k>0); assume(Tmax>Tmin); Te(t)=(Tmax+Tmin)/2+(Tmax-Tmin)/2*sin(w*t);
Now this is the differential equation solution:
sol=desolve(diff(T(t),t)-q+k*(T(t)-Te(t)),[T,t],[0,T0]);
The solution with q=0 for example would be
sol.subs(Tmax=21.6,Tmin=15.2,k=0.024,q=0,T0=15.6,w=pi/12);
but I need that q to be a model for a heater that's off from 8 AM to 22 PM, and on from 22 PM to 8 AM. So I need to define a q function that if t mod 24 is between 8 and 22 its value is 0, and 0.054 otherwise.
I've been trying with the piecewise function but it's not plotting anything, I always get error messages.
Thanks for your time.
plot differential-equations sage
asked Nov 24 '18 at 23:55
AbrahamlureAbrahamlure
1137
add a comment |
I need to solve a differential equation. The solution will depend on t and q, and I need to define that q piecewise depending on t.
var('k,Tmax,Tmin,w,T0,q'); T=function('T')(t); Te=function('Te')(t);
assume(k>0); assume(Tmax>Tmin); Te(t)=(Tmax+Tmin)/2+(Tmax-Tmin)/2*sin(w*t);
Now this is the differential equation solution:
sol=desolve(diff(T(t),t)-q+k*(T(t)-Te(t)),[T,t],[0,T0]);
The solution with q=0 for example would be
sol.subs(Tmax=21.6,Tmin=15.2,k=0.024,q=0,T0=15.6,w=pi/12);
but I need that q to be a model for a heater that's off from 8 AM to 22 PM, and on from 22 PM to 8 AM. So I need to define a q function that if t mod 24 is between 8 and 22 its value is 0, and 0.054 otherwise.
I've been trying with the piecewise function but it's not plotting anything, I always get error messages.
Thanks for your time.
plot differential-equations sage
asked Nov 24 '18 at 23:55
AbrahamlureAbrahamlure
1137
add a comment |
I need to solve a differential equation. The solution will depend on t and q, and I need to define that q piecewise depending on t.
var('k,Tmax,Tmin,w,T0,q'); T=function('T')(t); Te=function('Te')(t);
assume(k>0); assume(Tmax>Tmin); Te(t)=(Tmax+Tmin)/2+(Tmax-Tmin)/2*sin(w*t);
Now this is the differential equation solution:
sol=desolve(diff(T(t),t)-q+k*(T(t)-Te(t)),[T,t],[0,T0]);
The solution with q=0 for example would be
sol.subs(Tmax=21.6,Tmin=15.2,k=0.024,q=0,T0=15.6,w=pi/12);
but I need that q to be a model for a heater that's off from 8 AM to 22 PM, and on from 22 PM to 8 AM. So I need to define a q function that if t mod 24 is between 8 and 22 its value is 0, and 0.054 otherwise.
I've been trying with the piecewise function but it's not plotting anything, I always get error messages.
Thanks for your time.
plot differential-equations sage
asked Nov 24 '18 at 23:55
AbrahamlureAbrahamlure
1137
I need to solve a differential equation. The solution will depend on t and q, and I need to define that q piecewise depending on t.
var('k,Tmax,Tmin,w,T0,q'); T=function('T')(t); Te=function('Te')(t);
assume(k>0); assume(Tmax>Tmin); Te(t)=(Tmax+Tmin)/2+(Tmax-Tmin)/2*sin(w*t);
Now this is the differential equation solution:
sol=desolve(diff(T(t),t)-q+k*(T(t)-Te(t)),[T,t],[0,T0]);
The solution with q=0 for example would be
sol.subs(Tmax=21.6,Tmin=15.2,k=0.024,q=0,T0=15.6,w=pi/12);
but I need that q to be a model for a heater that's off from 8 AM to 22 PM, and on from 22 PM to 8 AM. So I need to define a q function that if t mod 24 is between 8 and 22 its value is 0, and 0.054 otherwise.
I've been trying with the piecewise function but it's not plotting anything, I always get error messages.
Thanks for your time.
plot differential-equations sage
plot differential-equations sage
asked Nov 24 '18 at 23:55
AbrahamlureAbrahamlure
1137
asked Nov 24 '18 at 23:55
AbrahamlureAbrahamlure
1137
edited Nov 25 '18 at 1:05
Abrahamlure
asked Nov 24 '18 at 23:55
AbrahamlureAbrahamlure
1137
asked Nov 24 '18 at 23:55
AbrahamlureAbrahamlure
1137
asked Nov 24 '18 at 23:55
AbrahamlureAbrahamlure
1137
1137
add a comment |
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
StackExchange.using("externalEditor", function () {
StackExchange.using("snippets", function () {
StackExchange.snippets.init();
});
});
}, "code-snippets");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "1"
};
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: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
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%2fstackoverflow.com%2fquestions%2f53463466%2fplotting-a-solution-of-a-differential-equation-with-sagemath%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Stack Overflow!
- 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.
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%2fstackoverflow.com%2fquestions%2f53463466%2fplotting-a-solution-of-a-differential-equation-with-sagemath%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
