Solving coupled differential equations with iterative method.

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I am trying to solve the following coupled differential equations:
and ,
where and .
The parameters here that I would like to tune are , and all other parameters are just constants. I have solved this using the finite difference method in Matlab, but this is innacurate because it is only a first order method. I am looking for a higher order algorithm to solve this pair of equations.

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R2021b

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