mathematics, the spectral theory of ordinary differential equations is the part of spectral theory concerned with the determination of the spectrum and...

applications, a Sturm–Liouville problem is a second-order linear ordinary differential equation of the form d d x [ p ( x ) d y d x ] + q ( x ) y = − λ w ( x...

distinct subfields. Ordinary differential equations can be viewed as a subclass of partial differential equations, corresponding to functions of a single variable...

Stochastic differential equations can also be extended to differential manifolds. Stochastic differential equations originated in the theory of Brownian...

for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In...

theory is a branch of the theory of ordinary differential equations relating to the class of solutions to periodic linear differential equations of the...

ordinary stochastic differential equations generalize ordinary differential equations. They have relevance to quantum field theory, statistical mechanics...

from linear algebra and matrix theory. Spectral theory of ordinary differential equations part of spectral theory concerned with the spectrum and eigenfunction...

theory, they can be applied to other branches of mathematics. Fractional differential equations, also known as extraordinary differential equations,...

Control theory Oscillation theory Spectral theory of ordinary differential equations Submarine signals "Charles-François Sturm | Number Theory, Geometry...

solution of partial differential equations. They are closely related to spectral methods, but complement the basis by an additional pseudo-spectral basis...

Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations. The...

state, i.e. partial differential equations (PDEs) which are infinite dimensional, as opposed to ordinary differential equations (ODEs) having a finite...

helped to develop the Spectral theory of ordinary differential equations. He worked especially on second-order singular differential operators with a continuous...

theory is a theory of integral equations. In the narrowest sense, Fredholm theory concerns itself with the solution of the Fredholm integral equation...

separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which...

In mathematics, in the field of ordinary differential equations, a nontrivial solution to an ordinary differential equation F ( x , y , y ′ ,   … ,   y...

The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system.: 1–2  Its...

transform eigenfunctions Hilbert–Schmidt theorem Spectral theory of ordinary differential equations Davydov 1976, p. 20. Kusse & Westwig 1998, p. 435...

existence theorem (ordinary differential equations) Picard–Lindelöf theorem (ordinary differential equations) Shift theorem (differential operators) Sturm–Picone...

of Classical Mechanics and Ordinary Differential Equations) and popular mathematics books, he influenced many mathematicians and physicists. Many of his...

following: a set of algebraic equations for steady-state problems; and a set of ordinary differential equations for transient problems. These equation sets are...

can still exhibit some chaotic properties. The above set of three ordinary differential equations has been referred to as the three-dimensional Lorenz model...

dynamical systems theory, topological field theories, stochastic differential equations (SDE), and the theory of pseudo-Hermitian operators. It can be seen...

fact, considered parts of mathematical physics, while other closely related fields are. For example, ordinary differential equations and symplectic geometry...

nature of the problem. In the case of differential equations, boundary conditions cannot be satisfied; in algebraic equations, the possible number of solutions...

information theory, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of the...

One way of finding such explicit solutions is to reduce the equations to equations of lower dimension, preferably ordinary differential equations, which...

The Lorenz system is a set of three ordinary differential equations, first developed by the meteorologist Edward Lorenz while studying atmospheric convection...

physics. In the theory of ordinary differential equations, spectral methods on a suitable Hilbert space are used to study the behavior of eigenvalues and...