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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 ]
The equations are written only for the small domain of individual elements of the structure rather than a single equation that describes the response of the system as a whole (a continuum). The latter would result in an intractable problem, hence the utility of the finite element method.
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.
The von Bertalanffy growth function (VBGF), or von Bertalanffy curve, is a type of growth curve for a time series and is named after Ludwig von Bertalanffy.It is a special case of the generalised logistic function.
They do not depend on the separability of the equations or other special properties of the equation. They have also been widely used for more-complicated non-symmetric and nonlinear systems of equations, like the Lamé equations of elasticity or the Navier-Stokes equations. [4]
In mathematics and numerical analysis, an adaptive step size is used in some methods for the numerical solution of ordinary differential equations (including the special case of numerical integration) in order to control the errors of the method and to ensure stability properties such as A-stability. Using an adaptive stepsize is of particular ...
When the differential equation is more complicated, say by having an inhomogeneous diffusion coefficient, the integral defining the element stiffness matrix can be evaluated by Gaussian quadrature. The condition number of the stiffness matrix depends strongly on the quality of the numerical grid. In particular, triangles with small angles in ...
These row operations are labelled in the table as +, +. Once y is also eliminated from the third row, the result is a system of linear equations in triangular form, and so the first part of the algorithm is complete. From a computational point of view, it is faster to solve the variables in reverse order, a process known as back-substitution.