Hi there. I have to solve a system of coupled ordinary differential equations. I have some initial values, but in different points of the domain. The equations are all first order. Lets suppose the system looks like this:(adsbygoogle = window.adsbygoogle || []).push({});

##\displaystyle\frac{dy_1}{dz}=y_1+y_2+0.01##

##\displaystyle\frac{dy_2}{dz}=y_1+y_2+0.01##

with initial conditions: ##y_1(0)=0, y_2(10)=0##

So, I use some discretization in z, and get some iteration scheme that looks like

##y_{1,n+1}=f_1(y_{1,n},y_{2,n})##

##y_{2,n+1}=f_2(y_{1,n},y_{2,n})##

I don't give exactly the recursion formula I've arrivesd I just simplified it to discuss the important aspects, ##f_1## and ##f_2## are just some functions. The thing is, that as you can see, the forward value depends in the current one for both solutions. So, the only way I can get a formula which I can solve is by setting the initial condition at the same point (lets say ##y_1(0)=0## and ##y_2(0)=0##), otherwise, I lack the information necessary to update the values in both solutions.

Does anyone know where I can find some examples on how to solve coupled differential equations with arbitrary initial values?

Best regards.

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# Numerical methods for a system of coupled ODE

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