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Conceptually, I understand how a numerical method like Monte Carlo is used to solve a definite integral. Because integral of a function is the area bounded by the curve, the ratio of random points that land inside the curve to the total number of points is the value of the integral.

Conceptually, can someone explain for a non math person, how we can solve a PDE/ODE using Monte Carlo?

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The trick is to convert ODE/PDE into an integral equation and then Monte Carlo comes to play. Here are some examples. http://jotterbach.github.io/2018/08/08/MonteCarloODE/

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  • $\begingroup$ Nice link! Thanks! $\endgroup$ – Esmailian Apr 2 '19 at 15:42

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