Using ode15i

I tried to solve an implicit differential equation of the form f = c1*q^4 + c2*dqdt^2 - c3 (where c1,c2,c3>0) with ode15i. The wanted solution oscillates, but the solution that I get doesn't. It does, though, stop about where it is supposed to, but not exactly. How can I get it right?

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Here is the relevant part of the code:

x0 = 0

v0 = 2

tspan=[0,6]

option = odeset('events', @condE);

[x0, v0] = decic(@diffE, tspan(1), x0, [], v0, []);

[t, xv, tf, xvf, ~] = ode15i(@diffE, tspan, x0, v0, option);

%% ODE function for energy equation

function f = diffE(~, q, dqdt)

% Assume: m = 1; k = 1; E = 1;

f = (m/2)*dqdt.^2 + (m*k/4)*q.^4 - E;

end

%% Event function for x0 = 0 for energy equation

function [val, ister, dir] = condE(~, ~, dxdt)

val = dxdt;

ister = 1;

dir = -1;

end

[Torsten]

The code is incomplete.

Answer 1

[Torsten]

Nothing oscillating can be seen:

https://www.wolframalpha.com/input/?i=Runge-Kutta+method,+dy%2Fdx+%3D+Sqrt(2-0.5*y(x)%5E4),+y(0)+%3D+0,+from+0+to+1.3,+h+%3D+.025

Best wishes

Torsten.

[Inbar Maimon]

When you differentiate you get the force eq. c2*d2q/dt2 = -4*c1*q^3, which oscillates.

I think it is reasonable, for there are only even powers in the conservation equation 0 = c1*q^4 + c2*dqdt^2 - c3 from which I began.

But yeah, that was exactly my problem. I tried taking the square root and realized that by doing so I force the solution to give only positive dq/dt.