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I need to utilize a Runge Kutta second order approach to solve two coupled first order DE's simultaneously given some initial conditions and a conservation relationship.

The DE's are as follows:

[tex]\frac{dp}{dt}[/tex] = aq - bp

[tex]\frac{dq}{dt}[/tex] = -aq + bp

Where a and b are constants, a=3, b=4, and the conservation relationship is n_{t}= p(t) + q(t). Here, n_{t}= 3.

I'm having trouble getting the ball rolling with writing the R.K. algorithm for this, will be programming in matlab. I have solved the equations analytically by hand and have found the following:

p(t) = -0.055972e^{-3t}+ 3.055972e^{-4}

q(t) = -0.055972e^{-7t}+ 3.055972

Any help on how to get started with the Runge Kutta algorithm to solve numerically would be appreciated!

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# Help! Programming Runge Kutta

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