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e. 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 ...
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 ...
A performance indicator or key performance indicator ( KPI) is a type of performance measurement. [1] KPIs evaluate the success of an organization or of a particular activity (such as projects, programs, products and other initiatives) in which it engages. [2] KPIs provide a focus for strategic and operational improvement, create an analytical ...
Meta-optimization. Meta-optimization concept. In numerical optimization, meta-optimization is the use of one optimization method to tune another optimization method. Meta-optimization is reported to have been used as early as in the late 1970s by Mercer and Sampson [1] for finding optimal parameter settings of a genetic algorithm .
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Stiff equation. In mathematics, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small. It has proven difficult to formulate a precise definition of stiffness, but the main idea is that the equation includes some terms ...
Dormand–Prince method. In numerical analysis, the Dormand–Prince ( RKDP) method or DOPRI method, is an embedded method for solving ordinary differential equations (ODE). [1] The method is a member of the Runge–Kutta family of ODE solvers. More specifically, it uses six function evaluations to calculate fourth- and fifth-order accurate ...
In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. [1] A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any ...