Exponential integrators can be constructed to be explicit or implicit for numerical ordinary differential equations or serve as the time integrator for...

equation is exact, but it doesn't define the integral. The first-order exponential integrator can be realized by holding N ( y ( t n + τ ) ) {\displaystyle {\mathcal...

numerical integrator to quickly achieve convergence. Like Gaussian quadrature, Tanh-Sinh quadrature is well suited for arbitrary-precision integration, where...

integral Exponential integrator Exponential map (Lie theory) Exponential map (Riemannian geometry) Exponential map (discrete dynamical systems) Exponential notation...

exponential nonlinearity is strongly supported by experimental evidence. In the adaptive exponential integrate-and-fire neuron the above exponential nonlinearity...

In biology exponential integrate-and-fire models are compact and computationally efficient nonlinear spiking neuron models with one or two variables....

Exponential growth occurs when a quantity grows as an exponential function of time. The quantity grows at a rate directly proportional to its present...

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems...

A fractional-order integrator or just simply fractional integrator is an integrator device that calculates the fractional-order integral or derivative...

In mathematics, the exponential integral Ei is a special function on the complex plane. It is defined as one particular definite integral of the ratio...

A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by...

Double exponential may refer to: A double exponential function Double exponential time, a task with time complexity roughly proportional to such a function...

exponential, also called the path-ordered exponential, is a mathematical operation defined in non-commutative algebras, equivalent to the exponential...

In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special...

symplectic integrator (SI) is a numerical integration scheme for Hamiltonian systems. Symplectic integrators form the subclass of geometric integrators which...

control theory, a continuous linear time-invariant system (LTI) is exponentially stable if and only if the system has eigenvalues (i.e., the poles of...

the weights in the exponential moving average which follows. An exponential moving average (EMA), also known as an exponentially weighted moving average...

Encyclopedia of Mathematics Implementations of many quadrature and cubature formulae within the free Tracker Component Library. SageMath Online Integrator...

system integrator integrates discrete systems utilizing a variety of techniques such as computer networking, enterprise application integration, business...

parameters Differential equations Product rule Quotient rule Exact differential Matrix exponential Munkhammar, Joakim, "Integrating Factor", MathWorld....

Lie groups, the exponential map is a map from the Lie algebra g of a Lie group G into G. In case G is a matrix Lie group, the exponential map reduces to...

important than the local error, and the Verlet integrator is therefore known as a second-order integrator. Systems of multiple particles with constraints...

Dynamic relaxation Geometric integrator — a method that preserves some geometric structure of the equation Symplectic integrator — a method for the solution...

is also used more generally to characterize any type of exponential (or, rarely, non-exponential) decay. For example, the medical sciences refer to the...

fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x, one has...

The following is a list of integrals of exponential functions. For a complete list of integral functions, please see the list of integrals. Indefinite...

any coefficient. Rule-based integration systems facilitate integration. Rubi, a computer algebra system rule-based integrator, pattern matches an extensive...

In mathematics, the exponential function can be characterized in many ways. This article presents some common characterizations, discusses why each makes...

and numerical analyst known for her research on matrix exponentials, exponential integrators, and their applications to the numerical solution of differential...

current-mode circuits that can be made using transistors that obey an exponential current-voltage characteristic—this includes bipolar junction transistors...