I have 3 coupled (implicit) ODE and 1 algebraic equation to be solved iteratively in two dimension. The algebraic equation output depends on the output of 3 ODEs. However, all ODE output does not depend on rest ODE output (initial value problem). I am trying to solve it using multivariate newton raphson technique (which works well for coupled ODE once they are converted into algebraic equation). However, i have extra algebraic equation. Please suggest me an algorithm which can solve it.
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