Solving second-order non-linear PDE
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I am trying to solve this second order differential equation

Where
θ is a function of space (x) and time (t),
κ is a function of space. This is a known ramp function that starts at 0 and increases to a fixed value.
v is constant and is

A is a constant.
With initial conditions at
of
, 



I have tried using pdepe but I am struggling to get it into a form that is acceptable. I have also attempted reformating it as an ODE but wasn't able to get any resonable solutions.
Is this a feasible equation that can be solved with Matlabs solvers?
Thanks
2 commentaires
Aditya Patil
le 12 Mai 2021
Can you verify the following? If v is constant and v = x/t, then theta is function of only t(or x), as x = vt. Similarly k is also function of t.
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Aditya Patil
le 13 Mai 2021
As per my understanding, the core issue here is with the variable k which needs to be saturated. In other words,
k = min(0, max(C, x))
For some constant C.
As a workaround, you can set the above condition in the odefun parameter of the solver, say ode45.
On a side note, you can also use Simulink. See the attached file for example.
t = [1:0.1:20];
x = sin(t);
input = [t;x]';
sim("differentialExample");
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