plt.plot(xaxes,errorlistforward,label="relative true error of forward difference approximation", color="g") plt.plot(xaxes,errorlistbackward,label="relative true ...

""" f: a vector of functions x: a n (>1) dimensional vector, where f(x) is evaluated. dx: a finite change in the given point method: use central-difference approximation by default; use ...

This paper analyzes a high-accuracy approximation to the $m$th-order linear ordinary differential equation $Mu = f$. At mesh points, $U$ is the estimate of $u$; and ...

We propose a method for numerical approximation of backward stochastic differential equations. Our method allows the final condition of the equation to be quite general and simple to implement. It ...

Abstract: One well-adopted power grid simulation methodology is to factorize matrix once and perform only backward/forward substitution with a deliberately chosen step size along the simulation. Since ...