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Inverting the matrix form of the Zoeppritz equations give the coefficients as a function of angle. Although the four equations can be solved for the four unknowns, they do not give an intuitive understanding for how the reflection amplitudes vary with the rock properties involved (density, velocity etc.). [3]
MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities.
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 ]
As suggested in the introduction, the Euler method is more accurate if the step size is smaller. The table below shows the result with different step sizes. The top row corresponds to the example in the previous section, and the second row is illustrated in the figure.
The step size is =. The same illustration for = The midpoint method converges faster than the Euler method, as .. Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs).
In statistics, a generalized estimating equation (GEE) is used to estimate the parameters of a generalized linear model with a possible unmeasured correlation between observations from different timepoints.
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 ...
Let be the state at time .For a decision that begins at time 0, we take as given the initial state .At any time, the set of possible actions depends on the current state; we express this as (), where a particular action represents particular values for one or more control variables, and () is the set of actions available to be taken at state .