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The Zoeppritz equations were not the first to describe the amplitudes of reflected and refracted waves at a plane interface. Cargill Gilston Knott used an approach in terms of potentials almost 20 years earlier, in 1899, to derive Knott's equations. Both approaches are valid, but Zoeppritz's approach is more easily understood. [2]
Plot of the Whittaker function M k,m(z) with k=2 and m= 1 / 2 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D In mathematics, a Whittaker function is a special solution of Whittaker's equation, a modified form of the confluent hypergeometric equation introduced by Whittaker () to make the formulas involving the solutions more ...
MATLAB (an abbreviation of "MATrix LABoratory" [22]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
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Pitzer equations [1] are important for the understanding of the behaviour of ions dissolved in natural waters such as rivers, lakes and sea-water. [ 2 ] [ 3 ] [ 4 ] They were first described by physical chemist Kenneth Pitzer . [ 5 ]
They can be applied naturally in a time-stepping solution of parabolic partial differential equations, or they can be applied directly to time-dependent partial differential equations. [12] Research on multilevel techniques for hyperbolic partial differential equations is underway. [ 13 ]
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CORDIC (coordinate rotation digital computer), Volder's algorithm, Digit-by-digit method, Circular CORDIC (Jack E. Volder), [1] [2] Linear CORDIC, Hyperbolic CORDIC (John Stephen Walther), [3] [4] and Generalized Hyperbolic CORDIC (GH CORDIC) (Yuanyong Luo et al.), [5] [6] is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots ...