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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...

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

stochastic differential equations. Stochastic differential equations can also be extended to differential manifolds. Stochastic differential equations originated...

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

smoothness of solutions to the Navier–Stokes equations, named as one of the Millennium Prize Problems in 2000. Partial differential equations are ubiquitous...

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

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

Eigenvalues and eigenvectors Hilbert–Schmidt theorem Spectral theory of ordinary differential equations Fixed point combinator Fourier transform eigenfunctions...

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

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...

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

heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric functions. The theory of the heat...

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

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

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

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

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

The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. It is notable for having...