ODE45 for Second Order

Question

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I have this second order ODE I am trying to solve w.r.t t (i.e d^2y/dt^2)

y'' = A/R[1-(1/c^2*(y')^2)]^1.5.

The initial value of y ( i.e y(0)) is a vector and y'(0) is a constant. Quantities A, R, and c are constants. I reduced it to a first order ODE as

y(1)' = A/R[1-(1/c^2*(y(1))^2)]^1.5

where y(1) = y' and wrote the script below:

A = 1.345e+8;
y0 = [0:10:2.5e-3];
y(1) = 2.5e-3;
c = 3e+4;
f = @(t,y) [y(2);((A/y)*(1-(y(1)/c^2)))];
tSpan = [0:10:50];
[t,y] = ode23(f,tSpan,y0)

but I keep getting an error. Please, what I did wrong? Thanks.

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Answer 1

James Tursa 2018-6-6

编辑：James Tursa 2018-6-6

1 个投票

Based on your description, I would have expected something more like this for the derivative:

R = 2.5e-3;
f = @(t,y) [y(2);(A/R)*(1-(y(2)^2/c^2))^1.5];

That being said, I don't follow what you mean by "y is a vector" and this initial condition:

y0 = [0:10:2.5e-3] <-- the stepping and final value don't make sense

Do you mean you want to solve this ODE independently for several different starting conditions?

James Tursa 2018-6-14

plot(t,y(:,1));

Shozeal 2018-6-14

Exactly what I am looking for, thanks a lot.