How to plot two functions together using odeplot?
$begingroup$
I'm trying to compare (graphically) approximations obtained using Euler's method and RK4-method.
ode := {diff(y(x), x) = 2*cos(x)*y(x), y(0) = 1};
p := dsolve(ode, y(x), numeric, method = classical[rk4], stepsize = .25);
f := dsolve(ode, y(x), numeric, method = classical[foreuler], stepsize = .25)
But can't plot them together.
plots:-odeplot([p, f], x = 0 .. 10);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
How can I solve this problem? Besides, I want to use style=point for "euler" curve, and plot exact solution on the same graph, if it's possible. What is the best method to obtain exact solution?
Any help would be appreciated.
ordinary-differential-equations maple
edited Dec 2 '18 at 17:21
LutzL
57.1k42054
asked Dec 2 '18 at 16:04
Kelly ShepphardKelly Shepphard
2298
$endgroup$
add a comment |
$begingroup$
I'm trying to compare (graphically) approximations obtained using Euler's method and RK4-method.
ode := {diff(y(x), x) = 2*cos(x)*y(x), y(0) = 1};
p := dsolve(ode, y(x), numeric, method = classical[rk4], stepsize = .25);
f := dsolve(ode, y(x), numeric, method = classical[foreuler], stepsize = .25)
But can't plot them together.
plots:-odeplot([p, f], x = 0 .. 10);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
How can I solve this problem? Besides, I want to use style=point for "euler" curve, and plot exact solution on the same graph, if it's possible. What is the best method to obtain exact solution?
Any help would be appreciated.
ordinary-differential-equations maple
edited Dec 2 '18 at 17:21
LutzL
57.1k42054
asked Dec 2 '18 at 16:04
Kelly ShepphardKelly Shepphard
2298
$endgroup$
$begingroup$
this seems to be more of a programming issue than a math one. Obviously it's applied to math in a programming language that's very much geared towards math, but I don't know how the community feels about debugging code.
$endgroup$
– Tyberius
Dec 2 '18 at 16:23
add a comment |
$begingroup$
I'm trying to compare (graphically) approximations obtained using Euler's method and RK4-method.
ode := {diff(y(x), x) = 2*cos(x)*y(x), y(0) = 1};
p := dsolve(ode, y(x), numeric, method = classical[rk4], stepsize = .25);
f := dsolve(ode, y(x), numeric, method = classical[foreuler], stepsize = .25)
But can't plot them together.
plots:-odeplot([p, f], x = 0 .. 10);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
How can I solve this problem? Besides, I want to use style=point for "euler" curve, and plot exact solution on the same graph, if it's possible. What is the best method to obtain exact solution?
Any help would be appreciated.
ordinary-differential-equations maple
edited Dec 2 '18 at 17:21
LutzL
57.1k42054
asked Dec 2 '18 at 16:04
Kelly ShepphardKelly Shepphard
2298
$endgroup$
I'm trying to compare (graphically) approximations obtained using Euler's method and RK4-method.
ode := {diff(y(x), x) = 2*cos(x)*y(x), y(0) = 1};
p := dsolve(ode, y(x), numeric, method = classical[rk4], stepsize = .25);
f := dsolve(ode, y(x), numeric, method = classical[foreuler], stepsize = .25)
But can't plot them together.
plots:-odeplot([p, f], x = 0 .. 10);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
How can I solve this problem? Besides, I want to use style=point for "euler" curve, and plot exact solution on the same graph, if it's possible. What is the best method to obtain exact solution?
Any help would be appreciated.
ordinary-differential-equations maple
ordinary-differential-equations maple
edited Dec 2 '18 at 17:21
LutzL
57.1k42054
asked Dec 2 '18 at 16:04
Kelly ShepphardKelly Shepphard
2298
edited Dec 2 '18 at 17:21
LutzL
57.1k42054
asked Dec 2 '18 at 16:04
Kelly ShepphardKelly Shepphard
2298
edited Dec 2 '18 at 17:21
LutzL
57.1k42054
edited Dec 2 '18 at 17:21
LutzL
57.1k42054
edited Dec 2 '18 at 17:21
LutzL
57.1k42054
57.1k42054
asked Dec 2 '18 at 16:04
Kelly ShepphardKelly Shepphard
2298
asked Dec 2 '18 at 16:04
Kelly ShepphardKelly Shepphard
2298
asked Dec 2 '18 at 16:04
Kelly ShepphardKelly Shepphard
2298
2298
$begingroup$
this seems to be more of a programming issue than a math one. Obviously it's applied to math in a programming language that's very much geared towards math, but I don't know how the community feels about debugging code.
$endgroup$
– Tyberius
Dec 2 '18 at 16:23
add a comment |
$begingroup$
this seems to be more of a programming issue than a math one. Obviously it's applied to math in a programming language that's very much geared towards math, but I don't know how the community feels about debugging code.
$endgroup$
– Tyberius
Dec 2 '18 at 16:23
$begingroup$
this seems to be more of a programming issue than a math one. Obviously it's applied to math in a programming language that's very much geared towards math, but I don't know how the community feels about debugging code.
$endgroup$
– Tyberius
Dec 2 '18 at 16:23
$begingroup$
this seems to be more of a programming issue than a math one. Obviously it's applied to math in a programming language that's very much geared towards math, but I don't know how the community feels about debugging code.
$endgroup$
– Tyberius
Dec 2 '18 at 16:23
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The key to answering you question is that you can produce the plots separately (using odeplot or plot), and then combine them together using the plots:-display command.
For fun, let's plot the two numeric methods with style=point, at the x-values that match the fixed step-size of the forward-Euler method.
I find it more convenient to use plot instead of plots:-odeplot here, after using the output=listprocedure option of dsolve (numeric).
restart;
ode := {diff(y(x), x) = 2*cos(x)*y(x), y(0) = 1}:
stpsz := .25;
stpsz := 0.25
a,b := 0, 10;
a, b := 0, 10
numpts := floor((b-a)/stpsz + 1);
numpts := 41
p := dsolve(ode, y(x), numeric, method = classical[rk4],
stepsize = stpsz, output=listprocedure):
f := dsolve(ode, y(x), numeric, method = classical[foreuler],
stepsize = stpsz, output=listprocedure):
e := dsolve(ode, y(x)):
Pe := plot(eval(y(x),e), x = a..b, style=line, legend="Exact"):
Pp := plot(eval(y(x),p), a..b, color=blue,
style=point, symbol=circle, symbolsize=10,
adaptive=false, numpoints=numpts, legend="RK4"):
Pf := plot(eval(y(x),f), a..b, color=green,
style=point, symbol=diagonalcross, symbolsize=10,
adaptive=false, numpoints=numpts, legend="For.Euler"):
plots:-display(Pe, Pp, Pf);
You can issue the commands eval(y(x),e) and eval(y(x),f) separately, to see that they are a syntax for picking off the RHS expression or procedure from the dsolve solution.
answered Dec 2 '18 at 17:35
aceracer
3,640199
$endgroup$
$begingroup$
Thank you very much, it was the best possible answer. Now it's clear for me how to plot graphs of approximations. :)
$endgroup$
– Kelly Shepphard
Dec 2 '18 at 17:42
add a comment |
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1 Answer
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active
oldest
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1 Answer
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$begingroup$
The key to answering you question is that you can produce the plots separately (using odeplot or plot), and then combine them together using the plots:-display command.
For fun, let's plot the two numeric methods with style=point, at the x-values that match the fixed step-size of the forward-Euler method.
I find it more convenient to use plot instead of plots:-odeplot here, after using the output=listprocedure option of dsolve (numeric).
restart;
ode := {diff(y(x), x) = 2*cos(x)*y(x), y(0) = 1}:
stpsz := .25;
stpsz := 0.25
a,b := 0, 10;
a, b := 0, 10
numpts := floor((b-a)/stpsz + 1);
numpts := 41
p := dsolve(ode, y(x), numeric, method = classical[rk4],
stepsize = stpsz, output=listprocedure):
f := dsolve(ode, y(x), numeric, method = classical[foreuler],
stepsize = stpsz, output=listprocedure):
e := dsolve(ode, y(x)):
Pe := plot(eval(y(x),e), x = a..b, style=line, legend="Exact"):
Pp := plot(eval(y(x),p), a..b, color=blue,
style=point, symbol=circle, symbolsize=10,
adaptive=false, numpoints=numpts, legend="RK4"):
Pf := plot(eval(y(x),f), a..b, color=green,
style=point, symbol=diagonalcross, symbolsize=10,
adaptive=false, numpoints=numpts, legend="For.Euler"):
plots:-display(Pe, Pp, Pf);
You can issue the commands eval(y(x),e) and eval(y(x),f) separately, to see that they are a syntax for picking off the RHS expression or procedure from the dsolve solution.
answered Dec 2 '18 at 17:35
aceracer
3,640199
$endgroup$
$begingroup$
Thank you very much, it was the best possible answer. Now it's clear for me how to plot graphs of approximations. :)
$endgroup$
– Kelly Shepphard
Dec 2 '18 at 17:42
add a comment |
$begingroup$
The key to answering you question is that you can produce the plots separately (using odeplot or plot), and then combine them together using the plots:-display command.
For fun, let's plot the two numeric methods with style=point, at the x-values that match the fixed step-size of the forward-Euler method.
I find it more convenient to use plot instead of plots:-odeplot here, after using the output=listprocedure option of dsolve (numeric).
restart;
ode := {diff(y(x), x) = 2*cos(x)*y(x), y(0) = 1}:
stpsz := .25;
stpsz := 0.25
a,b := 0, 10;
a, b := 0, 10
numpts := floor((b-a)/stpsz + 1);
numpts := 41
p := dsolve(ode, y(x), numeric, method = classical[rk4],
stepsize = stpsz, output=listprocedure):
f := dsolve(ode, y(x), numeric, method = classical[foreuler],
stepsize = stpsz, output=listprocedure):
e := dsolve(ode, y(x)):
Pe := plot(eval(y(x),e), x = a..b, style=line, legend="Exact"):
Pp := plot(eval(y(x),p), a..b, color=blue,
style=point, symbol=circle, symbolsize=10,
adaptive=false, numpoints=numpts, legend="RK4"):
Pf := plot(eval(y(x),f), a..b, color=green,
style=point, symbol=diagonalcross, symbolsize=10,
adaptive=false, numpoints=numpts, legend="For.Euler"):
plots:-display(Pe, Pp, Pf);
You can issue the commands eval(y(x),e) and eval(y(x),f) separately, to see that they are a syntax for picking off the RHS expression or procedure from the dsolve solution.
answered Dec 2 '18 at 17:35
aceracer
3,640199
$endgroup$
$begingroup$
Thank you very much, it was the best possible answer. Now it's clear for me how to plot graphs of approximations. :)
$endgroup$
– Kelly Shepphard
Dec 2 '18 at 17:42
add a comment |
$begingroup$
The key to answering you question is that you can produce the plots separately (using odeplot or plot), and then combine them together using the plots:-display command.
For fun, let's plot the two numeric methods with style=point, at the x-values that match the fixed step-size of the forward-Euler method.
I find it more convenient to use plot instead of plots:-odeplot here, after using the output=listprocedure option of dsolve (numeric).
restart;
ode := {diff(y(x), x) = 2*cos(x)*y(x), y(0) = 1}:
stpsz := .25;
stpsz := 0.25
a,b := 0, 10;
a, b := 0, 10
numpts := floor((b-a)/stpsz + 1);
numpts := 41
p := dsolve(ode, y(x), numeric, method = classical[rk4],
stepsize = stpsz, output=listprocedure):
f := dsolve(ode, y(x), numeric, method = classical[foreuler],
stepsize = stpsz, output=listprocedure):
e := dsolve(ode, y(x)):
Pe := plot(eval(y(x),e), x = a..b, style=line, legend="Exact"):
Pp := plot(eval(y(x),p), a..b, color=blue,
style=point, symbol=circle, symbolsize=10,
adaptive=false, numpoints=numpts, legend="RK4"):
Pf := plot(eval(y(x),f), a..b, color=green,
style=point, symbol=diagonalcross, symbolsize=10,
adaptive=false, numpoints=numpts, legend="For.Euler"):
plots:-display(Pe, Pp, Pf);
You can issue the commands eval(y(x),e) and eval(y(x),f) separately, to see that they are a syntax for picking off the RHS expression or procedure from the dsolve solution.
answered Dec 2 '18 at 17:35
aceracer
3,640199
$endgroup$
The key to answering you question is that you can produce the plots separately (using odeplot or plot), and then combine them together using the plots:-display command.
For fun, let's plot the two numeric methods with style=point, at the x-values that match the fixed step-size of the forward-Euler method.
I find it more convenient to use plot instead of plots:-odeplot here, after using the output=listprocedure option of dsolve (numeric).
restart;
ode := {diff(y(x), x) = 2*cos(x)*y(x), y(0) = 1}:
stpsz := .25;
stpsz := 0.25
a,b := 0, 10;
a, b := 0, 10
numpts := floor((b-a)/stpsz + 1);
numpts := 41
p := dsolve(ode, y(x), numeric, method = classical[rk4],
stepsize = stpsz, output=listprocedure):
f := dsolve(ode, y(x), numeric, method = classical[foreuler],
stepsize = stpsz, output=listprocedure):
e := dsolve(ode, y(x)):
Pe := plot(eval(y(x),e), x = a..b, style=line, legend="Exact"):
Pp := plot(eval(y(x),p), a..b, color=blue,
style=point, symbol=circle, symbolsize=10,
adaptive=false, numpoints=numpts, legend="RK4"):
Pf := plot(eval(y(x),f), a..b, color=green,
style=point, symbol=diagonalcross, symbolsize=10,
adaptive=false, numpoints=numpts, legend="For.Euler"):
plots:-display(Pe, Pp, Pf);
You can issue the commands eval(y(x),e) and eval(y(x),f) separately, to see that they are a syntax for picking off the RHS expression or procedure from the dsolve solution.
answered Dec 2 '18 at 17:35
aceracer
3,640199
answered Dec 2 '18 at 17:35
aceracer
3,640199
answered Dec 2 '18 at 17:35
aceracer
3,640199
answered Dec 2 '18 at 17:35
aceracer
3,640199
3,640199
$begingroup$
Thank you very much, it was the best possible answer. Now it's clear for me how to plot graphs of approximations. :)
$endgroup$
– Kelly Shepphard
Dec 2 '18 at 17:42
add a comment |
$begingroup$
Thank you very much, it was the best possible answer. Now it's clear for me how to plot graphs of approximations. :)
$endgroup$
– Kelly Shepphard
Dec 2 '18 at 17:42
$begingroup$
Thank you very much, it was the best possible answer. Now it's clear for me how to plot graphs of approximations. :)
$endgroup$
– Kelly Shepphard
Dec 2 '18 at 17:42
$begingroup$
Thank you very much, it was the best possible answer. Now it's clear for me how to plot graphs of approximations. :)
$endgroup$
– Kelly Shepphard
Dec 2 '18 at 17:42
add a comment |
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$begingroup$
this seems to be more of a programming issue than a math one. Obviously it's applied to math in a programming language that's very much geared towards math, but I don't know how the community feels about debugging code.
$endgroup$
– Tyberius
Dec 2 '18 at 16:23