As the title, Why more smooth the function the better finite difference method? I guess that if the function is smooth we can better approximate with Taylor series, but formally how this helps? ...
I'm interested in deriving a forward finite difference approximation for the gradient of a function, $f(x)$, at the point $x = x_i$ using $k+1$ points. If the spatial domain is uniformly discretized, ...
I am trying to find an analytical way to describe the finite difference coefficients of various degrees of accuracy of centred difference schemes that approximate the second derivative. For example, a ...
(Disclaimer: I'm a high school student, and my knowledge of mathematics extends only to some elementary high school calculus. I don't know if what I'm about to do is valid mathematics.) I noticed ...
I have a generic function $g(x)$ where $x$ is an 6-dimensional vector. Now I want to compute the Hessian of this function for a point $x_0$. What is the most efficient way to do this? Can I do this ...