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Lotka–Volterra equations. The Lotka–Volterra equations, also known as the Lotka–Volterra predator–prey model, are a pair of first-order nonlinear [disambiguation needed] differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey.
The non-random two-liquid model [1] (abbreviated NRTL model) is an activity coefficient model introduced by Renon and Prausnitz in 1968 that correlates the activity coefficients of a compound with its mole fractions in the liquid phase concerned. It is frequently applied in the field of chemical engineering to calculate phase equilibria.
Iterative method. In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n -th approximation is derived from the previous ones. A specific implementation with termination criteria for a given ...
This includes the whole left half of the complex plane, making it suitable for the solution of stiff equations. In fact, the backward Euler method is even L-stable. The region for a discrete stable system by Backward Euler Method is a circle with radius 0.5 which is located at (0.5, 0) in the z-plane. Extensions and modifications
Successive over-relaxation. In numerical linear algebra, the method of successive over-relaxation ( SOR) is a variant of the Gauss–Seidel method for solving a linear system of equations, resulting in faster convergence. A similar method can be used for any slowly converging iterative process .
In fact, nondimensionalization can suggest the parameters which should be used for analyzing a system. However, it is necessary to start with an equation that describes the system appropriately. Nondimensionalization steps. To nondimensionalize a system of equations, one must do the following: Identify all the independent and dependent variables;
DDEs are also called time-delay systems, systems with aftereffect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations. They belong to the class of systems with the functional state , i.e. partial differential equations (PDEs) which are infinite dimensional, as opposed to ordinary ...
Equating coefficients. In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of unknown parameters. It relies on the fact that two expressions are identical precisely when corresponding coefficients are equal for each different type of term.