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Codes for electromagnetic scattering by cylinders – this article list codes for electromagnetic scattering by a cylinder. Majority of existing codes for calculation of electromagnetic scattering by a single cylinder are based on Mie theory , which is an analytical solution of Maxwell's equations in terms of infinite series.
Several progressively more accurate approximations of the step function. An asymmetrical Gaussian function fit to a noisy curve using regression.. In general, a function approximation problem asks us to select a function among a well-defined class [citation needed] [clarification needed] that closely matches ("approximates") a target function [citation needed] in a task-specific way.
The algorithms studied here can be used to compute such an approximation. An alternative method is to use techniques from calculus to obtain a series expansion of the solution. Ordinary differential equations occur in many scientific disciplines, including physics , chemistry , biology , and economics . [ 1 ]
Let us now apply Euler's method again with a different step size to generate a second approximation to y(t n+1). We get a second solution, which we label with a ( 1 ) {\displaystyle (1)} . Take the new step size to be one half of the original step size, and apply two steps of Euler's method.
At the remaining critical point (0, 0) the second derivative test is insufficient, and one must use higher order tests or other tools to determine the behavior of the function at this point. (In fact, one can show that f takes both positive and negative values in small neighborhoods around (0, 0) and so this point is a saddle point of f .)
As a result, at the point , where the accuracy of the approximation may be the worst in the ordinary Padé approximation, good accuracy of the 2-point Padé approximant is guaranteed. Therefore, the 2-point Padé approximant can be a method that gives a good approximation globally for x = 0 ∼ ∞ {\displaystyle x=0\sim \infty } .
The Remez algorithm or Remez exchange algorithm, published by Evgeny Yakovlevich Remez in 1934, is an iterative algorithm used to find simple approximations to functions, specifically, approximations by functions in a Chebyshev space that are the best in the uniform norm L ∞ sense. [1]
In mathematics, the method of matched asymptotic expansions [1] is a common approach to finding an accurate approximation to the solution to an equation, or system of equations. It is particularly used when solving singularly perturbed differential equations. It involves finding several different approximate solutions, each of which is valid (i ...