Finding all roots to equation [duplicate]
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 Dec 9 at 10:58
wznd
315
marked as duplicate by Szabolcs, Daniel Lichtblau, AccidentalFourierTransform, Michael E2 equation-solving
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Dec 9 at 18:17
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 |
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 Dec 9 at 10:58
wznd
315
marked as duplicate by Szabolcs, Daniel Lichtblau, AccidentalFourierTransform, Michael E2 equation-solving
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Dec 9 at 18:17
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
Dec 9 at 15:14
@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
Dec 9 at 22:25
@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
Dec 9 at 23:58
add a comment |
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 Dec 9 at 10:58
wznd
315
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 Dec 9 at 10:58
wznd
315
asked Dec 9 at 10:58
wznd
315
asked Dec 9 at 10:58
wznd
315
asked Dec 9 at 10:58
wznd
315
asked Dec 9 at 10:58
wznd
315
315
marked as duplicate by Szabolcs, Daniel Lichtblau, AccidentalFourierTransform, Michael E2 equation-solving
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Dec 9 at 18:17
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Dec 9 at 18:17
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
Dec 9 at 15:14
@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
Dec 9 at 22:25
@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
Dec 9 at 23:58
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
Dec 9 at 15:14
@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
Dec 9 at 22:25
@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
Dec 9 at 23:58
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
Dec 9 at 15:14
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
Dec 9 at 15:14
@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
Dec 9 at 22:25
@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
Dec 9 at 22:25
@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
Dec 9 at 23:58
@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
Dec 9 at 23:58
add a comment |
1 Answer
1
active
oldest
votes
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 Dec 9 at 12:05
zhk
8,80411433
When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
– wznd
Dec 9 at 12:34
@wznd You should input the interval of interest.
– zhk
Dec 9 at 12:38
@wznd. For meNSolveandFindAllCrossingsworks fine,I checked on Mathematica10.2and11.3.
– Mariusz Iwaniuk
Dec 9 at 12:50
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
Dec 9 at 14:28
1
@MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
– zhk
Dec 9 at 14:35
|
show 2 more comments
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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 Dec 9 at 12:05
zhk
8,80411433
When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
– wznd
Dec 9 at 12:34
@wznd You should input the interval of interest.
– zhk
Dec 9 at 12:38
@wznd. For meNSolveandFindAllCrossingsworks fine,I checked on Mathematica10.2and11.3.
– Mariusz Iwaniuk
Dec 9 at 12:50
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
Dec 9 at 14:28
1
@MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
– zhk
Dec 9 at 14:35
|
show 2 more comments
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 Dec 9 at 12:05
zhk
8,80411433
When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
– wznd
Dec 9 at 12:34
@wznd You should input the interval of interest.
– zhk
Dec 9 at 12:38
@wznd. For meNSolveandFindAllCrossingsworks fine,I checked on Mathematica10.2and11.3.
– Mariusz Iwaniuk
Dec 9 at 12:50
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
Dec 9 at 14:28
1
@MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
– zhk
Dec 9 at 14:35
|
show 2 more comments
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 Dec 9 at 12:05
zhk
8,80411433
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 Dec 9 at 12:05
zhk
8,80411433
edited Dec 9 at 12:44
answered Dec 9 at 12:05
zhk
8,80411433
answered Dec 9 at 12:05
zhk
8,80411433
answered Dec 9 at 12:05
zhk
8,80411433
8,80411433
When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
– wznd
Dec 9 at 12:34
@wznd You should input the interval of interest.
– zhk
Dec 9 at 12:38
@wznd. For meNSolveandFindAllCrossingsworks fine,I checked on Mathematica10.2and11.3.
– Mariusz Iwaniuk
Dec 9 at 12:50
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
Dec 9 at 14:28
1
@MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
– zhk
Dec 9 at 14:35
|
show 2 more comments
When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
– wznd
Dec 9 at 12:34
@wznd You should input the interval of interest.
– zhk
Dec 9 at 12:38
@wznd. For meNSolveandFindAllCrossingsworks fine,I checked on Mathematica10.2and11.3.
– Mariusz Iwaniuk
Dec 9 at 12:50
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
Dec 9 at 14:28
1
@MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
– zhk
Dec 9 at 14:35
When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
– wznd
Dec 9 at 12:34
When i try NSolve i get nothing back as output? Also, the FindAllCrossings isn't working either.
– wznd
Dec 9 at 12:34
@wznd You should input the interval of interest.
– zhk
Dec 9 at 12:38
@wznd You should input the interval of interest.
– zhk
Dec 9 at 12:38
@wznd. For me
NSolve and FindAllCrossings works fine,I checked on Mathematica 10.2 and 11.3.– Mariusz Iwaniuk
Dec 9 at 12:50
@wznd. For me
NSolve and FindAllCrossings works fine,I checked on Mathematica 10.2 and 11.3.– Mariusz Iwaniuk
Dec 9 at 12:50
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
Dec 9 at 14:28
@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
Dec 9 at 14:28
1
1
@MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
– zhk
Dec 9 at 14:35
@MichaelE2 "11.0.1 for Microsoft Windows (32-bit)"
– zhk
Dec 9 at 14:35
|
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
Dec 9 at 15:14
@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
Dec 9 at 22:25
@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
Dec 9 at 23:58