Random Walk, Laplace Equation, Poisson Equation, Brownian Motion, Maxwell Boltzmann.
2-D Laplace equation Let me illustrate the random walk method by choosing a toy problem whose analytical solution is known as We can easily show that (5) is a solution of (4) because the second derivative of (5) with respect to x is 2 and that with respect to y is -2. Moreover, we can show that a