Derive the standard five point formula for Poisson equation with one-dimensional spacing h and k in x and y directions respectively.
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- Find the moment generating function for Y. c=4compute the first-order partial derivatives. Q = reθIf the eigenvalues from a linearized system of non-linear differential equations indicate a fixed point at the origin is an unstable spiral, yet the non-linearized system shows that a limit cycle exists at the circle r=1, do we still classify the origin as an unstable spiral even though it approaches the limit cycle? In other words, does an unstable spiral have to approach infinity as time increases? Or can we say an unstable spiral approaches a limit cycle? I'm wondering how do we classify the stability of the origin when a limit cycle exists? Hope this makes sense.