Finding all roots to equation [duplicate]
up vote
2
down vote
favorite
This question already has an answer here:
About multi-root search in Mathematica for transcendental equations
8 answers
I'm currently doing some Mathematica exercises, and I'm stuck on this one task where you're supposed to plot the functions h(t)= |3-t^2|+|t-1|-t^2 , g(t)=3sin(t)
in the same grap, and then find all the roots. This is what I've got so far:
The instructions say that I should use FindRoot to exactly decide all the roots, but I don't think I've done it right. What should I change with the function in order to make it find all of the roots?
Thanks in advance.
plotting equation-solving
asked 21 hours ago
wznd
182
marked as duplicate by Szabolcs, Daniel Lichtblau, AccidentalFourierTransform, Michael E2 equation-solving
Users with the equation-solving badge can single-handedly close equation-solving questions as duplicates and reopen them as needed.
StackExchange.ready(function() {
if (StackExchange.options.isMobile) return;
$('.dupe-hammer-message-hover:not(.hover-bound)').each(function() {
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');
$hover.hover(
function() {
$hover.showInfoMessage('', {
messageElement: $msg.clone().show(),
transient: false,
position: { my: 'bottom left', at: 'top center', offsetTop: -7 },
dismissable: false,
relativeToBody: true
});
},
function() {
StackExchange.helpers.removeMessages();
}
);
});
});
13 hours ago
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
up vote
2
down vote
favorite
This question already has an answer here:
About multi-root search in Mathematica for transcendental equations
8 answers
I'm currently doing some Mathematica exercises, and I'm stuck on this one task where you're supposed to plot the functions h(t)= |3-t^2|+|t-1|-t^2 , g(t)=3sin(t)
in the same grap, and then find all the roots. This is what I've got so far:
The instructions say that I should use FindRoot to exactly decide all the roots, but I don't think I've done it right. What should I change with the function in order to make it find all of the roots?
Thanks in advance.
plotting equation-solving
asked 21 hours ago
wznd
182
marked as duplicate by Szabolcs, Daniel Lichtblau, AccidentalFourierTransform, Michael E2 equation-solving
Users with the equation-solving badge can single-handedly close equation-solving questions as duplicates and reopen them as needed.
StackExchange.ready(function() {
if (StackExchange.options.isMobile) return;
$('.dupe-hammer-message-hover:not(.hover-bound)').each(function() {
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');
$hover.hover(
function() {
$hover.showInfoMessage('', {
messageElement: $msg.clone().show(),
transient: false,
position: { my: 'bottom left', at: 'top center', offsetTop: -7 },
dismissable: false,
relativeToBody: true
});
},
function() {
StackExchange.helpers.removeMessages();
}
);
});
});
13 hours ago
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
Solve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]works for me in V11.3, but notNSolvefor some reason.
– Michael E2
16 hours ago
@MichaelE2 - I would guess thatNSolveuses a derivative and cannot handleAbs. Since the values are real, a workaround isNSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t] /. Abs[z_] :> Sqrt[z^2], -5 <= t <= 5}, t]
– Bob Hanlon
9 hours ago
@BobHanlon You can see in the comments to @zhk's answer below thatNSolveworks in earlier versions of Mma. While there's some plausibility in your suggestion, it stills seems a backslide.
– Michael E2
8 hours ago
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
This question already has an answer here:
About multi-root search in Mathematica for transcendental equations
8 answers
I'm currently doing some Mathematica exercises, and I'm stuck on this one task where you're supposed to plot the functions h(t)= |3-t^2|+|t-1|-t^2 , g(t)=3sin(t)
in the same grap, and then find all the roots. This is what I've got so far:
The instructions say that I should use FindRoot to exactly decide all the roots, but I don't think I've done it right. What should I change with the function in order to make it find all of the roots?
Thanks in advance.
plotting equation-solving
asked 21 hours ago
wznd
182
This question already has an answer here:
About multi-root search in Mathematica for transcendental equations
8 answers
I'm currently doing some Mathematica exercises, and I'm stuck on this one task where you're supposed to plot the functions h(t)= |3-t^2|+|t-1|-t^2 , g(t)=3sin(t)
in the same grap, and then find all the roots. This is what I've got so far:
The instructions say that I should use FindRoot to exactly decide all the roots, but I don't think I've done it right. What should I change with the function in order to make it find all of the roots?
Thanks in advance.
This question already has an answer here:
About multi-root search in Mathematica for transcendental equations
8 answers
plotting equation-solving
plotting equation-solving
asked 21 hours ago
wznd
182
asked 21 hours ago
wznd
182
asked 21 hours ago
wznd
182
asked 21 hours ago
wznd
182
asked 21 hours ago
wznd
182
182
marked as duplicate by Szabolcs, Daniel Lichtblau, AccidentalFourierTransform, Michael E2 equation-solving
Users with the equation-solving badge can single-handedly close equation-solving questions as duplicates and reopen them as needed.
StackExchange.ready(function() {
if (StackExchange.options.isMobile) return;
$('.dupe-hammer-message-hover:not(.hover-bound)').each(function() {
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');
$hover.hover(
function() {
$hover.showInfoMessage('', {
messageElement: $msg.clone().show(),
transient: false,
position: { my: 'bottom left', at: 'top center', offsetTop: -7 },
dismissable: false,
relativeToBody: true
});
},
function() {
StackExchange.helpers.removeMessages();
}
);
});
});
13 hours ago
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by Szabolcs, Daniel Lichtblau, AccidentalFourierTransform, Michael E2 equation-solving
Users with the equation-solving badge can single-handedly close equation-solving questions as duplicates and reopen them as needed.
StackExchange.ready(function() {
if (StackExchange.options.isMobile) return;
$('.dupe-hammer-message-hover:not(.hover-bound)').each(function() {
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');
$hover.hover(
function() {
$hover.showInfoMessage('', {
messageElement: $msg.clone().show(),
transient: false,
position: { my: 'bottom left', at: 'top center', offsetTop: -7 },
dismissable: false,
relativeToBody: true
});
},
function() {
StackExchange.helpers.removeMessages();
}
);
});
});
13 hours ago
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
Solve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]works for me in V11.3, but notNSolvefor some reason.
– Michael E2
16 hours ago
@MichaelE2 - I would guess thatNSolveuses a derivative and cannot handleAbs. Since the values are real, a workaround isNSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t] /. Abs[z_] :> Sqrt[z^2], -5 <= t <= 5}, t]
– Bob Hanlon
9 hours ago
@BobHanlon You can see in the comments to @zhk's answer below thatNSolveworks in earlier versions of Mma. While there's some plausibility in your suggestion, it stills seems a backslide.
– Michael E2
8 hours ago
add a comment |
Solve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]works for me in V11.3, but notNSolvefor some reason.
– Michael E2
16 hours ago
@MichaelE2 - I would guess thatNSolveuses a derivative and cannot handleAbs. Since the values are real, a workaround isNSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t] /. Abs[z_] :> Sqrt[z^2], -5 <= t <= 5}, t]
– Bob Hanlon
9 hours ago
@BobHanlon You can see in the comments to @zhk's answer below thatNSolveworks in earlier versions of Mma. While there's some plausibility in your suggestion, it stills seems a backslide.
– Michael E2
8 hours ago
Solve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t] works for me in V11.3, but not NSolve for some reason.– Michael E2
16 hours ago
Solve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t] works for me in V11.3, but not NSolve for some reason.– Michael E2
16 hours ago
@MichaelE2 - I would guess that
NSolve uses a derivative and cannot handle Abs. Since the values are real, a workaround is NSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t] /. Abs[z_] :> Sqrt[z^2], -5 <= t <= 5}, t]– Bob Hanlon
9 hours ago
@MichaelE2 - I would guess that
NSolve uses a derivative and cannot handle Abs. Since the values are real, a workaround is NSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t] /. Abs[z_] :> Sqrt[z^2], -5 <= t <= 5}, t]– Bob Hanlon
9 hours ago
@BobHanlon You can see in the comments to @zhk's answer below that
NSolve works in earlier versions of Mma. While there's some plausibility in your suggestion, it stills seems a backslide.– Michael E2
8 hours ago
@BobHanlon You can see in the comments to @zhk's answer below that
NSolve works in earlier versions of Mma. While there's some plausibility in your suggestion, it stills seems a backslide.– Michael E2
8 hours ago
add a comment |
1 Answer
1
active
oldest
votes
up vote
5
down vote
You can use NSolve to find multiple roots,
NSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]
{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}
or FindAllCrossings from here,
FindAllCrossings[Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], {t, -10, 10},
WorkingPrecision -> 20]
{-4.9295434376879868373, -3.7745180124835511931, 0.76290087955924483126, 3.3574487606850113852}
or FindRoot providing good initial guesses,
FindRoot[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t]}, {t, #}] & /@ {-5, -3, 1, 4}
{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}
answered 19 hours ago
zhk
8,64911433
When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
– wznd
19 hours ago
@wznd You should input the interval of interest.
– zhk
19 hours ago
@wznd. For meNSolveandFindAllCrossingsworks fine,I checked on Mathematica10.2and11.3.
– Mariusz Iwaniuk
19 hours ago
1
@MichaelE2. With little modification works on MMA11.3:NSolve[{RealAbs[3 - t^2] + RealAbs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]
– Mariusz Iwaniuk
17 hours ago
1
@MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
– zhk
17 hours ago
|
show 2 more comments
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
5
down vote
You can use NSolve to find multiple roots,
NSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]
{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}
or FindAllCrossings from here,
FindAllCrossings[Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], {t, -10, 10},
WorkingPrecision -> 20]
{-4.9295434376879868373, -3.7745180124835511931, 0.76290087955924483126, 3.3574487606850113852}
or FindRoot providing good initial guesses,
FindRoot[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t]}, {t, #}] & /@ {-5, -3, 1, 4}
{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}
answered 19 hours ago
zhk
8,64911433
When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
– wznd
19 hours ago
@wznd You should input the interval of interest.
– zhk
19 hours ago
@wznd. For meNSolveandFindAllCrossingsworks fine,I checked on Mathematica10.2and11.3.
– Mariusz Iwaniuk
19 hours ago
1
@MichaelE2. With little modification works on MMA11.3:NSolve[{RealAbs[3 - t^2] + RealAbs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]
– Mariusz Iwaniuk
17 hours ago
1
@MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
– zhk
17 hours ago
|
show 2 more comments
up vote
5
down vote
You can use NSolve to find multiple roots,
NSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]
{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}
or FindAllCrossings from here,
FindAllCrossings[Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], {t, -10, 10},
WorkingPrecision -> 20]
{-4.9295434376879868373, -3.7745180124835511931, 0.76290087955924483126, 3.3574487606850113852}
or FindRoot providing good initial guesses,
FindRoot[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t]}, {t, #}] & /@ {-5, -3, 1, 4}
{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}
answered 19 hours ago
zhk
8,64911433
When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
– wznd
19 hours ago
@wznd You should input the interval of interest.
– zhk
19 hours ago
@wznd. For meNSolveandFindAllCrossingsworks fine,I checked on Mathematica10.2and11.3.
– Mariusz Iwaniuk
19 hours ago
1
@MichaelE2. With little modification works on MMA11.3:NSolve[{RealAbs[3 - t^2] + RealAbs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]
– Mariusz Iwaniuk
17 hours ago
1
@MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
– zhk
17 hours ago
|
show 2 more comments
up vote
5
down vote
up vote
5
down vote
You can use NSolve to find multiple roots,
NSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]
{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}
or FindAllCrossings from here,
FindAllCrossings[Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], {t, -10, 10},
WorkingPrecision -> 20]
{-4.9295434376879868373, -3.7745180124835511931, 0.76290087955924483126, 3.3574487606850113852}
or FindRoot providing good initial guesses,
FindRoot[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t]}, {t, #}] & /@ {-5, -3, 1, 4}
{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}
answered 19 hours ago
zhk
8,64911433
You can use NSolve to find multiple roots,
NSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]
{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}
or FindAllCrossings from here,
FindAllCrossings[Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], {t, -10, 10},
WorkingPrecision -> 20]
{-4.9295434376879868373, -3.7745180124835511931, 0.76290087955924483126, 3.3574487606850113852}
or FindRoot providing good initial guesses,
FindRoot[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t]}, {t, #}] & /@ {-5, -3, 1, 4}
{{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}}
answered 19 hours ago
zhk
8,64911433
edited 19 hours ago
answered 19 hours ago
zhk
8,64911433
answered 19 hours ago
zhk
8,64911433
answered 19 hours ago
zhk
8,64911433
8,64911433
When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
– wznd
19 hours ago
@wznd You should input the interval of interest.
– zhk
19 hours ago
@wznd. For meNSolveandFindAllCrossingsworks fine,I checked on Mathematica10.2and11.3.
– Mariusz Iwaniuk
19 hours ago
1
@MichaelE2. With little modification works on MMA11.3:NSolve[{RealAbs[3 - t^2] + RealAbs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]
– Mariusz Iwaniuk
17 hours ago
1
@MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
– zhk
17 hours ago
|
show 2 more comments
When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
– wznd
19 hours ago
@wznd You should input the interval of interest.
– zhk
19 hours ago
@wznd. For meNSolveandFindAllCrossingsworks fine,I checked on Mathematica10.2and11.3.
– Mariusz Iwaniuk
19 hours ago
1
@MichaelE2. With little modification works on MMA11.3:NSolve[{RealAbs[3 - t^2] + RealAbs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]
– Mariusz Iwaniuk
17 hours ago
1
@MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
– zhk
17 hours ago
When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
– wznd
19 hours ago
When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
– wznd
19 hours ago
@wznd You should input the interval of interest.
– zhk
19 hours ago
@wznd You should input the interval of interest.
– zhk
19 hours ago
@wznd. For me
NSolve and FindAllCrossings works fine,I checked on Mathematica 10.2 and 11.3.– Mariusz Iwaniuk
19 hours ago
@wznd. For me
NSolve and FindAllCrossings works fine,I checked on Mathematica 10.2 and 11.3.– Mariusz Iwaniuk
19 hours ago
1
1
@MichaelE2. With little modification works on MMA
11.3: NSolve[{RealAbs[3 - t^2] + RealAbs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]– Mariusz Iwaniuk
17 hours ago
@MichaelE2. With little modification works on MMA
11.3: NSolve[{RealAbs[3 - t^2] + RealAbs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]– Mariusz Iwaniuk
17 hours ago
1
1
@MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
– zhk
17 hours ago
@MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
– zhk
17 hours ago
|
show 2 more comments
Solve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], -5 <= t <= 5}, t]works for me in V11.3, but notNSolvefor some reason.– Michael E2
16 hours ago
@MichaelE2 - I would guess that
NSolveuses a derivative and cannot handleAbs. Since the values are real, a workaround isNSolve[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t] /. Abs[z_] :> Sqrt[z^2], -5 <= t <= 5}, t]– Bob Hanlon
9 hours ago
@BobHanlon You can see in the comments to @zhk's answer below that
NSolveworks in earlier versions of Mma. While there's some plausibility in your suggestion, it stills seems a backslide.– Michael E2
8 hours ago