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how to couple two time dependent physics equation?

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in a time step the result from the first equation is use to the second equation ? and then the next step the result of second equation is used to the first equation.
for example :



a(u1)*du1/dt+du2/dt=d^2(u1)/dx^2
b(u1)*du2/dt+du1/dt=d^2(u2)/dx^2

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