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A generalization of the Runge-Kutta method for solution of ordinary differential equations, also called Kaps-Rentrop methods.

The index of a vector field with finitely many zeros on a compact, oriented manifold is the same as the Euler characteristic of the manifold.

T-integration, which stands for "tunable numerical integration," is a fast, accurate, and numerically stable numerical integration formula given by ...

A method of stochastic optimization including techniques such as gradient search or Robbins-Monro stochastic approximation.

For discrete problems in which no efficient solution method is known, it might be necessary to test each possibility sequentially in order to determine if it is the solution. ...

It is thought that the totient valence function N_phi(m)>=2, i.e., if there is an n such that phi(n)=m, then there are at least two solutions n. This assertion is called ...

The Fourier transform is a generalization of the complex Fourier series in the limit as L->infty. Replace the discrete A_n with the continuous F(k)dk while letting n/L->k. ...

Chebyshev iteration is a method for solving nonsymmetric problems (Golub and van Loan 1996, §10.1.5; Varga, 1962, Ch. 5). Chebyshev iteration avoids the computation of inner ...

The following three pieces of information completely determine the homeomorphic type of a surface (Massey 1996): 1. Orientability, 2. Number of boundary components, 3. Euler ...

A method of displaying simple statistical parameters including hinges, the statistical median, and upper and lower values.