MATLAB: How to solve differential equation with variable input parameters

differential equationsMATLABvelocity array

How to solve differential equation: zdot = (w*v*z)+1. where w=constant, v= velocity array of size 10, z is the initial condition=0. The solution for the first step is the z value for the next step.

Best Answer

z0=0
z1=z0+dt*(w*v1*z1+1) -> z1=(z0+dt)/(1-dt*w*v1)
z2=z1+dt*(w*v2*z2+1) -> z2=(z1+dt)/(1-dt*w*v2)
...
In general:
Use the recursion
z(i+1)=(z(i)+dt)/(1-dt*w*v(i+1)) (i=1,...,9)
with
z(1)=0
Best wishes
Torsten.
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