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e. In mathematics, a differential-algebraic system of equations ( DAE) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system. The set of the solutions of such a system is a differential algebraic variety, and corresponds to an ideal in a differential algebra of ...
Matrix differential equation. A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. A matrix differential equation contains more than one function stacked into vector form with a matrix relating the functions to ...
Collocation method. In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations. The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain ...
Lorenz system. A sample solution in the Lorenz attractor when ρ = 28, σ = 10, and β = 8 3. The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions.
In mathematics, an ordinary differential equation ( ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown (s) consists of one (or more) function (s) and involves the derivatives of those functions. [1] The term "ordinary" is used in contrast with partial differential equations (PDEs ...
The Adomian decomposition method (ADM) is a semi-analytical method for solving ordinary and partial nonlinear differential equations. The method was developed from the 1970s to the 1990s by George Adomian, chair of the Center for Applied Mathematics at the University of Georgia. [1] It is further extensible to stochastic systems by using the ...
Integro-differential equations have found applications in epidemiology, the mathematical modeling of epidemics, particularly when the models contain age-structure or describe spatial epidemics. The Kermack-McKendrick theory of infectious disease transmission is one particular example where age-structure in the population is incorporated into ...
Backward differentiation formula. The backward differentiation formula ( BDF) is a family of implicit methods for the numerical integration of ordinary differential equations. They are linear multistep methods that, for a given function and time, approximate the derivative of that function using information from already computed time points ...