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Accurate evaluation of the function is a classic problem in numerical analysis. This function can be seen as an approximation to the first derivative of at , . More generally, is the divided difference of at and and this fact … Continue reading
In the previous post, Complex Magic, Part 1, the use of complex variables in approximating the first derivative of a holomorphic function was discussed. This post delves deeper and introduces formulas suitable for approximating the th derivative of a holomorphic … Continue reading
At the heart of conventional methods of derivative approximation based on divided differences lies a sum of the form in which the coefficients have different signs and vary (usually considerably) in magnitude. As a result, when these coefficients of different … Continue reading
The usefulness of nested functions in MATLAB has been the subject of heated debate (check out the comments in Loren Shure’s post Nested Functions and Variable Scope for instance) mainly due to the complexity of data flow. This is not … Continue reading
The following function (from L.N. Trefethen, Spectral Methods in MATLAB, with slight modifications) solves the 2nd order wave equation in 2 dimensions () using spectral methods, Fourier for x and Chebyshev for y direction. On its rectangular domain, the equation … Continue reading