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Longer titles found: Numerical methods for ordinary differential equations (view), Spectral theory of ordinary differential equations (view)

searching for Ordinary differential equation 79 found (323 total)

alternate case: ordinary differential equation

Linear stability (764 words) [view diff] no match in snippet view article find links to article

In mathematics, in the theory of differential equations and dynamical systems, a particular stationary or quasistationary solution to a nonlinear system

Probit (1,447 words) [view diff] exact match in snippet view article find links to article

Another means of computation is based on forming a non-linear ordinary differential equation (ODE) for probit, as per the Steinbrecher and Shaw method. Abbreviating

Forcing function (differential equations) (183 words) [view diff] exact match in snippet view article

is the forcing function in the nonhomogeneous, second-order, ordinary differential equation: a y ″ + b y ′ + c y = f ( t ) {\displaystyle ay''+by'+cy=f(t)}

Timeline of classical mechanics (1,933 words) [view diff] exact match in snippet view article find links to article

hanging chain by solving an ordinary differential equation 1734 - Daniel Bernoulli solves the ordinary differential equation for the vibrations of an elastic

Joseph Slepian (313 words) [view diff] case mismatch in snippet view article find links to article

thesis On the Functions of a Complex Variable Defined by an Ordinary Differential Equation of the First Order and First Degree advised by George Birkhoff

Logistic map (5,737 words) [view diff] exact match in snippet view article find links to article

of both periodic and chaotic solutions, whereas the logistic ordinary differential equation (ODE) exhibits regular solutions, commonly referred to as the

Comparison function (552 words) [view diff] exact match in snippet view article find links to article

\varepsilon {\text{-}}\delta } language. As an example, consider an ordinary differential equation where f : R n → R n {\displaystyle f:{\mathbb {R} }^{n}\to {\mathbb

Abstract differential equation (1,944 words) [view diff] no match in snippet view article find links to article

or wave equations) and all the others are put together, an ordinary "differential" equation with respect to the variable which was put in evidence is obtained

1739 in science (219 words) [view diff] exact match in snippet view article find links to article

Ocean. Leonhard Euler solves the general homogeneous linear ordinary differential equation with constant coefficients. Euler invents the tonnetz (German

Violet B. Haas (891 words) [view diff] exact match in snippet view article find links to article

(MIT). Her dissertation was titled Singular perturbations of an ordinary differential equation. Norman Levinson was her doctoral advisor. She met her future

First-order (376 words) [view diff] exact match in snippet view article find links to article

First-order stochastic dominance First order stream Exact first-order ordinary differential equation First-order differential equation First-order differential operator

Variance-stabilizing transformation (852 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\frac {dg}{d\mu }}={\frac {C}{\sqrt {h(\mu )}}}} This ordinary differential equation has, by separation of variables, the following solution: g (

System equivalence (910 words) [view diff] no match in snippet view article find links to article

sort of wave (partial differential) equation, or oscillator (ordinary differential) equation. Furthermore, these sorts of systems follow the capacitor or

Sinc numerical methods (428 words) [view diff] exact match in snippet view article find links to article

integration, approximate solution of initial and boundary value ordinary differential equation (ODE) problems, approximation and inversion of Fourier and Laplace

Limit cycle (1,216 words) [view diff] case mismatch in snippet view article find links to article

Analysis (Second ed.). SIAM. ISBN 9780898715262. Philip Hartman, "Ordinary Differential Equation", Society for Industrial and Applied Mathematics, 2002. Witold

Painlevé paradox (928 words) [view diff] exact match in snippet view article find links to article

sliding. The dynamical equations are then a particular singular ordinary differential equation with vector field f(x)/g(x), where both f and g may vanish at

Universal differential equation (696 words) [view diff] case mismatch in snippet view article find links to article

Pouly, Amaury; Bournez, Olivier (2020-02-28). "A Universal Ordinary Differential Equation". Logical Methods in Computer Science. 16 (1). arXiv:1702.08328

Groundwater model (2,023 words) [view diff] exact match in snippet view article find links to article

of Richards' equation partial differential equation, or the ordinary differential equation Finite Water-Content method as validated for modeling groundwater

Rayleigh problem (883 words) [view diff] exact match in snippet view article find links to article

Substituting this the partial differential equation, reduces it to ordinary differential equation f ″ + 1 2 η f ′ = 0 {\displaystyle f''+{\frac {1}{2}}\eta f'=0}

Stokes problem (1,980 words) [view diff] exact match in snippet view article find links to article

Substituting this into the partial differential equation reduces it to ordinary differential equation f ″ − i ω ν f = 0 {\displaystyle f''-{\frac {i\omega }{\nu }}f=0}

Joan E. Walsh (527 words) [view diff] exact match in snippet view article find links to article

century. Walsh conducted research into the numerical solution of ordinary differential equation boundary value problems and partial differential equations.

Bloch equations (3,276 words) [view diff] exact match in snippet view article find links to article

{dM_{xy}'(t)}{dt}}=-{\frac {M_{xy}'}{T_{2}}}} This is a linear ordinary differential equation and its solution is M x y ′ ( t ) = M x y ′ ( 0 ) e − t / T

Robert Emden (809 words) [view diff] exact match in snippet view article find links to article

The Lane-Emden equation can be described as "a second-order ordinary differential equation that applies to polytropic profiles in density". The Lane-Emden

Southwell plot (659 words) [view diff] exact match in snippet view article find links to article

problem whose mathematical analog is the same fourth order ordinary differential equation as above, with similar boundary conditions, the first eigenvalue

Berman flow (1,133 words) [view diff] exact match in snippet view article find links to article

{\displaystyle f(0)=f''(0)=f(1)-1=f'(1)=0} This third order nonlinear ordinary differential equation requires three boundary condition and the fourth boundary condition

C. K. Raju (850 words) [view diff] exact match in snippet view article find links to article

convert a retarded functional differential equation into an ordinary differential equation. C.K. Raju. Electromagnetic Time, chapter 5b, p.116-35 in Raju

Rigorous coupled-wave analysis (1,020 words) [view diff] exact match in snippet view article find links to article

transforms the partial differential equation into a matrix valued ordinary differential equation as a function of height over the periodic media. The finite

Mitio Nagumo (541 words) [view diff] exact match in snippet view article find links to article

3792/pia/1195581383 Nagumo, Mitio (1944), "On the periodic solution of an ordinary differential equation of second order", Zenkoku Shijou Suugaku Danwakai: 54–61 Nagumo

Vivienne Malone-Mayes (1,036 words) [view diff] exact match in snippet view article find links to article

the other studies the long-term behavior of a certain linear ordinary differential equation. Nonetheless, her research was sufficiently innovative for her

Boundary layer (7,490 words) [view diff] exact match in snippet view article find links to article

reduces the parabolic thermal boundary-layer equation to an ordinary differential equation. The solution to this equation, the temperature at any point

Hill's muscle model (1,761 words) [view diff] exact match in snippet view article find links to article

represents the muscle activation. It is defined based on the ordinary differential equation: d a ( t ) d t = 1 τ r i s e ( 1 − a ( t ) u ( t ) + 1 τ f a

Coronal seismology (1,482 words) [view diff] exact match in snippet view article find links to article

longitudinal direction have been studied theoretically. A second order ordinary differential equation has been derived describing the displacement of the loop axis

Blast wave (2,458 words) [view diff] exact match in snippet view article find links to article

radius of the blast wave) and t (time) to be transformed into an ordinary differential equation in terms of the similarity variable r 5 ρ o t 2 E {\displaystyle

Structural analysis (3,015 words) [view diff] exact match in snippet view article find links to article

materials problems, which require at most the solution of an ordinary differential equation. The finite element method is perhaps the most restrictive and

Acceptance testing (2,414 words) [view diff] exact match in snippet view article find links to article

Simpson, T. Ian (December 15, 2022). "Comparison of rule- and ordinary differential equation-based dynamic model of DARPP-32 signalling network". PeerJ.

Gaspard Monge (2,059 words) [view diff] exact match in snippet view article find links to article

had never presented itself to him. Monge's paper gives the ordinary differential equation of the curves of curvature, and establishes the general theory

Bayesian estimation of templates in computational anatomy (4,326 words) [view diff] exact match in snippet view article find links to article

and Eulerian specification of the flow fields satisfying the ordinary differential equation: with v ≐ ( v 1 , v 2 , v 3 ) {\displaystyle v\doteq (v_{1}

SAAM II (1,278 words) [view diff] case mismatch in snippet view article find links to article

pharmacological systems. SAAM II utilizes three types of integrators for Ordinary Differential Equation (ODE) solving: RK 4-5th order: A 4th-5th order Runge-Kutta methods

Quartic interaction (3,128 words) [view diff] exact match in snippet view article find links to article

=p\cdot x} . Then, the partial differential equation becomes an ordinary differential equation that is the one defining the Jacobi elliptic function with p

Internal wave (3,377 words) [view diff] exact match in snippet view article find links to article

k>0,} the equations in each layer reduces to a second-order ordinary differential equation in z {\displaystyle z} . Insisting on bounded solutions the

Jacobi's formula (2,102 words) [view diff] exact match in snippet view article find links to article

e^{tB}} The desired result follows as the solution to this ordinary differential equation. Several forms of the formula underlie the Faddeev–LeVerrier

Peter Onumanyi (1,093 words) [view diff] exact match in snippet view article find links to article

and P. Onumanyi (1985). An accurate collocation method for ordinary differential equation. Advances in Modelling and Simulation, Vol.4, pp. 45-58. Published

Alexander Munro Davie (918 words) [view diff] exact match in snippet view article find links to article

exponentially small estimate for a boundary value arising from an ordinary differential equation". Proceedings of the Royal Society of Edinburgh Section A: Mathematics

Bayesian model of computational anatomy (3,931 words) [view diff] exact match in snippet view article find links to article

and Eulerian specification of the flow fields satisfying the ordinary differential equation: with v ≐ ( v 1 , v 2 , v 3 ) {\displaystyle v\doteq (v_{1}

Bucket argument (3,624 words) [view diff] exact match in snippet view article find links to article

={\frac {\mathrm {d} h}{\mathrm {d} r}}\ ,} leading to the ordinary differential equation for the shape of the surface: d h d r = Ω 2 r g , {\displaystyle

Owl Scientific Computing (1,290 words) [view diff] exact match in snippet view article find links to article

on Functional Programming 2019, on the topics of numerical ordinary differential equation solving, and executing Owl computation on GPUs. An internship

Bass diffusion model (2,872 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \ q} is the coefficient of imitation Expressed as an ordinary differential equation, d F d t = p ( 1 − F ) + q ( 1 − F ) F = ( 1 − F ) ( p + q F

Characteristic impedance (4,069 words) [view diff] exact match in snippet view article find links to article

Doing so causes the time dependence to factor out, leaving an ordinary differential equation for the coefficients, which will be phasors, dependent on position

Biharmonic map (2,287 words) [view diff] exact match in snippet view article find links to article

solution of a certain constant-coefficient fourth-order linear ordinary differential equation for a ℝ4-valued function. As such the situation can be completely

Hyperpolarized carbon-13 MRI (1,974 words) [view diff] exact match in snippet view article find links to article

between the two species can then be modeled using the linear ordinary differential equation d M P d t ( t ) = − R 1 P M P ( t ) + k SP M S ( t ) {\displaystyle

Bring radical (8,543 words) [view diff] exact match in snippet view article find links to article

solution of the differential resolvent, being a fourth order ordinary differential equation, depends on four constants of integration, which should be chosen

Spray (mathematics) (2,388 words) [view diff] exact match in snippet view article

{L}}_{[V,H]-H}J} of the induced non-linear connection through the ordinary differential equation L V ϵ + ϵ = τ Θ V . {\displaystyle {\mathcal {L}}_{V}\epsilon

Classical control theory (1,801 words) [view diff] case mismatch in snippet view article find links to article

classical control theory uses the Laplace transform to change an Ordinary Differential Equation (ODE) in the time domain into a regular algebraic polynomial

RNA velocity (898 words) [view diff] exact match in snippet view article find links to article

accessibility and gene expression . DeepVelo is a neural network–based ordinary differential equation that can model complex transcriptome dynamics by describing

Maximum principle (3,699 words) [view diff] exact match in snippet view article find links to article

already seen in the one-dimensional case. For instance, the ordinary differential equation y″ + 2y = 0 has sinusoidal solutions, which certainly have interior

Mie–Grüneisen equation of state (2,261 words) [view diff] exact match in snippet view article find links to article

0 / d V {\displaystyle p_{0}=-de_{0}/dV} , we get The above ordinary differential equation can be solved for e0 with the initial condition e0 = 0 when

Screw theory (4,394 words) [view diff] exact match in snippet view article find links to article

From the definition of the matrix [S], we can formulate the ordinary differential equation, [ T ˙ ( t ) ] = [ S ] [ T ( t ) ] , {\displaystyle [{\dot {T}}(t)]=[S][T(t)]

Constraint (computational chemistry) (4,518 words) [view diff] exact match in snippet view article

equations and reduces the problem once again to solving an ordinary differential equation. Such an approach is used, for example, in describing the motion

Rotordynamics (2,267 words) [view diff] exact match in snippet view article find links to article

the system, we can create the following second-order linear ordinary differential equation that describes the radial deflection of the disk from the rotor

Degenerate energy levels (6,123 words) [view diff] exact match in snippet view article find links to article

^{2}}{2m}}{\frac {d^{2}\psi }{dx^{2}}}+V\psi =E\psi } Since this is an ordinary differential equation, there are two independent eigenfunctions for a given energy

Timeline of mathematics (7,723 words) [view diff] exact match in snippet view article find links to article

1739 – Leonhard Euler solves the general homogeneous linear ordinary differential equation with constant coefficients. 1742 – Christian Goldbach conjectures

Complex affine space (2,538 words) [view diff] exact match in snippet view article find links to article

the set of solutions of a second-order inhomogeneous linear ordinary differential equation (over the complex numbers). Finally, in analogy with the one-dimensional

COVID-19 pandemic on Diamond Princess (7,205 words) [view diff] exact match in snippet view article find links to article

longer range. With the application of the overall model (an ordinary differential equation-based Susceptible-Exposed-Infected-Recovery (SEIR) model with

Fokker–Planck equation (6,474 words) [view diff] exact match in snippet view article find links to article

splitting probabilities can be reduced to the solution of an ordinary differential equation which is intimately related to the Fokker–Planck equation. In

Hankel transform (4,184 words) [view diff] exact match in snippet view article find links to article

z^{2}}}\right\}=-k^{2}U+{\frac {\partial ^{2}}{\partial z^{2}}}U,} which is an ordinary differential equation in the transformed variable U {\displaystyle U} . The Bessel

Computational anatomy (16,865 words) [view diff] exact match in snippet view article find links to article

specification of the flow fields as first introduced in, satisfying the ordinary differential equation: with v ≐ ( v 1 , v 2 , v 3 ) {\displaystyle v\doteq (v_{1}

Metabolic network modelling (5,355 words) [view diff] exact match in snippet view article find links to article

simulation with such a network it is necessary to construct an ordinary differential equation system that describes the rates of change in each metabolite's

Lagrangian coherent structure (10,166 words) [view diff] exact match in snippet view article find links to article

reduced shrink lines. (Strictly speaking, this equation is not an ordinary differential equation, given that its right-hand side is not a vector field, but a

Beltrami equation (10,901 words) [view diff] exact match in snippet view article find links to article

locally in the analytic case by reducing the Beltrami to an ordinary differential equation in the complex domain. Here is a cookbook presentation of Gauss's

Spinodal decomposition (6,219 words) [view diff] exact match in snippet view article find links to article

}}}[f''+2\eta ^{2}Y+2Y\beta ^{2}]\beta ^{2}A(\beta )} This is an ordinary differential equation that has the solution: A(β,t)=A(β,0)exp⁡[R(β)t]{\displaystyle

Atmospheric entry (12,752 words) [view diff] exact match in snippet view article find links to article

formulas). The Lighthill-Freeman model is based upon a single ordinary differential equation and one algebraic equation. The five species model is based

History of physics (14,028 words) [view diff] exact match in snippet view article find links to article

could escape from them. In 1739, Leonhard Euler solved the ordinary differential equation for a forced harmonic oscillator and noticed the resonance phenomenon

Bouc–Wen model of hysteresis (3,485 words) [view diff] exact match in snippet view article find links to article

the Bouc–Wen–Baber–Noori model is given by: This is a stiff ordinary differential equation that can be solved, for example, using the function ode15 of

Rayleigh–Kuo criterion (3,267 words) [view diff] exact match in snippet view article find links to article

derived, is known as Rayleigh's equation which is a linear ordinary differential equation. It is very difficult to explicitly solve this equation. It

Riemannian metric and Lie bracket in computational anatomy (3,650 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \varphi _{t},t\in [0,1]} , generated via the ordinary differential equation with the Eulerian vector fields v ≐ ( v 1 , v 2 , v 3 ) {\displaystyle

Bending of plates (8,494 words) [view diff] exact match in snippet view article find links to article

{d^{2}Y_{m}}{dy^{2}}}+{\frac {m^{4}\pi ^{4}}{a^{4}}}Y_{m}=0\,.} This is an ordinary differential equation which has the general solution Y m = A m cosh ⁡ m π y a + B

Diffeomorphometry (3,615 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \varphi _{t},t\in [0,1]} , generated via the ordinary differential equation with the Eulerian vector fields v ≐ ( v 1 , v 2 , v 3 ) {\displaystyle

Large deformation diffeomorphic metric mapping (7,244 words) [view diff] exact match in snippet view article find links to article

Eulerian specification of the flow field associated to the ordinary differential equation, d d t φ t = v t ∘ φ t , φ 0 = i d , {\displaystyle {\frac

Outline of oceanography (32,647 words) [view diff] exact match in snippet view article find links to article

result of the Coriolis effect Taylor–Goldstein equation – An ordinary differential equation used in the field of fluid dynamics Telepresence technology