Applying updated initial conditions at every points of tspan and solve system of ODE using ode45

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AkB 2023-3-24

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评论： Torsten 2023-3-25

I am solving 6 ODEs (3 are of 2nd order and 3 are of 1st order) simultaneously. I need my code to be such that the initial condition is applied at each points of tspan (say, tspan=t0, t1, t2, t3.....tn) instead of only at t=t0. Moreover, initial conditions at each points of tspan need to be updated based of results of ODEs at the previous time step.

Mathematically, my eqns are (in much simplified manner):

d2xdt2= u1+vp*p1 ;

d2ydt2= u2+vp*p2 ;

d2zdt2= u3+vp*p3 ;

dp1dt= a1*p1+a2*p2+a3*p3 ;

dp2dt= b1*p1+b2*p2+b3*p3 ;

dp3dt= c1*p1+c2*p2+c3*p3 ;

Here, a1, a2, a3, b1, b2 b3, c1, c2, c3 and vp are constants, and u1, u2, and u3 are some functions of (x, y, z, t).

Initial condition: y0_a=[0 v1_ini 0 v2_ini 0 v3_ini_3 p1_0 p2_0 p3_0]

Now, with this I am getting a result wherein the value of v1=dxdt is v1=v1_ini at t=t0, however, for t > t0, v1 drops (please refer image attached).

I want : y0_a to be updated at each points of tspan=(t0, t1, t2, t3.....tn) according to

v1_ini (ti) = u0x + vp * p1(ti)

v1_ini (ti+1) = u0x + vp * p1(ti+1)....and so on. [u0x is a constant.]

Basically, I am simulating a microswimmer and it's velocity never drops down and it's velocity depends on instantaneous values of p=(p1, p2, p3). I have tried creating a for loop to update the initial value, but it repeats same value. Please see the attached code.

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Answer 1

Torsten 2023-3-24

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Then why do you solve for v1 if you want to prescribe it ? Simply set

v1 = u0x + vp*p1

in your code and determine displacement via

dx/dt = v1

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Torsten 2023-3-25

Instead I need to get a solution that where initial conditions at each time step is u0x+vp*p1(t), where p1(t) will be calculated simultaneously from ODEs involving dpdt.

This is the same as if you prescribe v1 = u0x + vp*p1 in my opinion. Or do you see any difference ?

Torsten 2023-3-25

Giving initial values at each step by an explicit formula means: prescribing the variable. And if you prescribe an initial value for v of v = uf(0)+vp*p or v = uf(t)+vp*p means: you set the variable v to uf(0)+vp*p resp. uf(t)+vp*p.

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