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You can solveit using standard numerical methods to solve a differential equation by breaking the difference equation using finite element methods. The method you use to solve it depends on the type of equations you expect to solve. Like for equations which turn out to be linear in terms of its variables can be solved like methods like Gauss Seidel Method. For equations that are non linear in terms of its variable methods like Newton Raphson or Bisection methods may be suitable.
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