ode45 with a array of vector
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I am solving 6 ODEs simultaneously. My eqns are:
eq1 = diff(x,t) == u1+vp.*p1 ;
eq2 = diff(y,t) == u2+vp.*p2 ;
eq3 = diff(z,t) == u3+vp.*p3 ;
eq1 = diff(p1,t) == a1*p1+a2*p2+a3*p3 ;
eq2 = diff(p2,t) == b1*p1+b2*p2+b3*p3 ;
eq3 = diff(p3,t) == c1*p1+c2*p2+c3*p3 ;
Here, a1, a2, a3, b1, b2 b3, c1, c2, c3 and vp are constants.
u1, u2, and u3 are vector of dimension [1 X 100]. Each values of u1, u2, and u3 corresponds to time points in tValues = linspace(0,10,100). I want to compute p1, p2, p3 and x, y, z for tValues = linspace(0,10,100).
My code is following: ;
vars = [x(t); z(t); y(t); p1(t); p2(t); p3(t)];
V = odeToVectorField([eq2 eq1 eq3 eq4 eq5 eq6]);
M = matlabFunction(V,'vars', {'t','Y'});
y0=[0 0 0 p1_0 p2_0 p3_0];
ySol_a = ode45(M,interval,y0);
Once the code is run, it shows following error message:
MuPAD error: Error: Cannot convert the initial value problem to an equivalent dynamical system. Either the differential equations cannot be solved for the highest derivatives or inappropriate initial conditions were specified. [numeric::ode2vectorfield]
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Accepted Answer
Torsten
on 23 Mar 2023
a1 = ...;
a2 = ...;
a3 = ...;
b1 = ...;
b2 = ...;
b3 = ...;
c1 = ...;
c2 = ...;
c3 = ...;
vp = ...;
tValues = linspace(0,10,100);
u1Values = ...;
u2Values = ...;
u3Values = ...;
u1fun = @(t)interp1(tValues,u1Values,t);
u2fun = @(t)interp1(tValues,u2Values,t);
u3fun = @(t)interp1(tValues,u3Values,t);
fun = @(t,y)[u1fun(t)+vp*y(4);u2fun(t)+vp*y(5);u3fun(t)+vp*y(6);a1*y(4)+a2*y(5)+a3*y(6);b1*y(4)+b2*y(5)+b3*y(6);c1*y(4)+c2*y(5)+c3*y(6)];
tspan = tValues;
p1_0 = ...;
p2_0 = ...;
p3_0 = ...;
y0 = [0 0 0 p1_0 p2_0 p3_0];
[T,Y] = ode45(fun,tspan,y0);
plot(T,Y)
6 Comments
Torsten
on 25 Mar 2023
How do I provide this dynamic initial condition?
I think I answered this already. An initial condition is not dynamic.
If you want to set
v1(t) = constant1 + vp*p1,
v2(t) = constant2 + vp*p2,
v3(t) = constant3 + vp*p3
your equations to integrate become
diff(x,t) = constant1 + vp*p1
diff(y,t) = constant2 + vp*p2
diff(z,t) = constant3 + vp*p3
diff(p1,t) == JTx_1+JTx_2+JTx_3;
diff(p2,t) == JTy_1+JTy_2+JTy_3;
diff(p3,t) == JTz_1+JTz_2+JTz_3;
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