X-Nico

unusual facts about differential equations



Numerical Recipes

The Numerical Recipes books cover a range of topics that include both classical numerical analysis (interpolation, integration, linear algebra, differential equations, and so on), signal processing (Fourier methods, filtering), statistical treatment of data, and a few topics in machine learning (hidden Markov models, support vector machines).


see also

Adomian

Adomian decomposition method, for solving differential equations, developed by George

Applications of the calculus of variations

Finite element method is a variational method for finding approximate solutions to boundary value problems in differential equations.

Arieh Iserles

He studied at the Hebrew University of Jerusalem and Ben-Gurion University of the Negev and wrote his PhD dissertation on numerical methods for stiff ordinary differential equations.

Birkhoff–Kellogg invariant-direction theorem

The Birkhoff–Kellogg theorem and its generalizations by Schauder and Leray have applications to partial differential differential equations.

Bocher

Maxime Bôcher (1867–1918), American mathematician who published about 100 papers on differential equations, series, and algebra

Brouwer fixed-point theorem

The theorem was first studied in view of work on differential equations by the French mathematicians around Poincaré and Picard.

Carl Gustav Jacob Jacobi

He also made fundamental contributions in the study of differential equations and to rational mechanics, notably the Hamilton–Jacobi theory.

Decomposition method

Domain decomposition methods in mathematics, numerical analysis, and numerical partial differential equations

Adomian decomposition method, a non-numerical method for solving nonlinear differential equations

Delay line

Bi-directional delay line, a numerical analysis technique used in computer simulation for solving ordinary differential equations by converting them to hyperbolic equations

Exact solutions in general relativity

With sufficiently clever assumptions of this sort, it is often possible to reduce the Einstein field equation to a much simpler system of equations, even a single partial differential equation (as happens in the case of stationary axisymmetric vacuum solutions, which are characterized by the Ernst equation) or a system of ordinary differential equations (as happens in the case of the Schwarzschild vacuum).

Forest Ray Moulton

The crater Moulton on the Moon, the Adams-Moulton methods for solving differential equations and the Moulton plane in geometry are named after him.

Franz Rellich

He studied from 1924 to 1929 at the universities of Graz and Göttingen and received his doctor's degree in 1929 under Richard Courant at Georg August University of Göttingen with the thesis about "Verallgemeinerung der Riemannschen Integrationsmethode auf Differentialgleichungen n-ter Ordnung in zwei Veränderlichen" ("Generalization of Riemann's integration method on differential equations of n-th order in two variables").

Gabriel Kron

In Fiji he had finished, and buried, Treatise on Differential Equations by Forsyth.

John Hymers

In particular, his Differential Equations and the Calculus of Finite Differences (1839) incorporated the new solution of the Laplacian equation for the figure of the earth as given by Thomas Gaskin in symbolic form; it was the elaboration of this original solution by Robert Leslie Ellis in 1841 which led largely to George Boole's masterpiece On a general method in analysis in 1844 (PRS, 5, 1843–50).

Journal of Hyperbolic Differential Equations

The Journal of Hyperbolic Differential Equations was founded in 2004 and carries papers pertaining to nonlinear hyperbolic problems and related mathematical topics, specifically on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics.

Mass matrix

Lagrangian mechanics yields an ordinary differential equation (actually, a system of coupled differential equations) that describes the evolution of a system in terms of an arbitrary vector of generalized coordinates that completely defines the position of every particle in the system.

Mathematical analysis

Poisson, Liouville, Fourier and others studied partial differential equations and harmonic analysis.

Mathieu wavelet

In 1868, the French mathematician Émile Léonard Mathieu introduced a family of differential equations nowadays termed Mathieu equations.

Method of moments

Boundary element method, a method of solving partial differential equations, that is often referred to as method of moments in electromagnetics

Monge–Ampère equation

Gilbarg, D. and Trudinger, N. S. Elliptic Partial Differential Equations of Second Order. Berlin: Springer-Verlag, 1983.

Mortar

Mortar methods, discretization methods for partial differential equations

Nick Katz

In 1978 he was an invited speaker at the International Congress of Mathematicians in Helsinki (p-adic L functions, Serre-Tate local moduli and ratios of solutions of differential equations) and 1970 in Nice (The regularity theorem in algebraic geometry).

Ordinary differential equation

Many mathematicians have studied differential equations and contributed to the field, including Newton, Leibniz, the Bernoulli family, Riccati, Clairaut, d'Alembert, and Euler.

Petrovsky

Petrovsky lacuna, mathematical concept in the field of partial differential equations

Riemann invariant

Riemann invariants are constant along the characteristic curves of the partial differential equations where they obtain the name invariant.

Subbaramiah Minakshisundaram

Kerala, 1968 August 13) was an Indian mathematician who worked on heat kernels and parabolic partial differential equations and introduced the Minakshisundaram–Pleijel zeta function.

Surface wave

Green function, a function used to solve inhomogeneous differential equations subject to boundary conditions.

Transmission line

The telegrapher's equations (or just telegraph equations) are a pair of linear differential equations which describe the voltage and current on an electrical transmission line with distance and time.

Tricomi

Francesco Tricomi (1897–1978), Italian mathematician famous for his studies on mixed type partial differential equations