Solving a nonlinear equation numerically

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Nivedita Tanksali
Nivedita Tanksali le 29 Oct 2020
I want to solve the nonlinear equation d^2(x)/dt^2 +(k)sinx = 0, numerically.
alternatively, this can be written as

Réponses (1)

John D'Errico
John D'Errico le 29 Oct 2020
It looks as if you don't need to solve it numerically.
syms x(t)
xpp = diff(x,t,2)
syms k
dsolve(xpp + k*sin(x) == 0)
dsolve(xpp + k*sin(x) == 0)
ans =
0
2*jacobiAM((2^(1/2)*(C1 - k)^(1/2)*(C2 - t)*1i)/2, -(2*k)/(C1 - k))
-2*jacobiAM((2^(1/2)*(C1 - k)^(1/2)*(C2 - t)*1i)/2, -(2*k)/(C1 - k))
Of course, it would help if you had some initial or boundary conditions. Then you might get a better answer.
But if you really, really need to solve it numerically, then you need to start with a tool like ODE45, and you need to pose a set of initial conditions, etc. As well, you need to define the value of k. No numerical solution can be found unless you specify k as a NUMBER.
  2 commentaires
Nivedita Tanksali
Nivedita Tanksali le 30 Oct 2020
The method that you've written the code for, what kind of method is it exactly?
as for boundary conditions,as im trying to solve the equation of motion for a nonlinear pendulum, i would think x=[0,pi/2] could be used.
The value of K is indeed a number, so that's not a problem.
Nivedita Tanksali
Nivedita Tanksali le 30 Oct 2020
also, the initial conditions are that is, initial displacement is the amplitude
and and initial circular velocity is 0

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