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A predictor-corrector method for solution of ordinary differential equations. The third-order equations for predictor and corrector are y_(n+1) = ...

A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the parabolas of parabolic cylindrical coordinates about the x-axis, ...

A general set of methods for integrating ordinary differential equations. Predictor-corrector methods proceed by extrapolating a polynomial fit to the derivative from the ...

The differential equation describing exponential growth is (dN)/(dt)=rN. (1) This can be integrated directly int_(N_0)^N(dN)/N=int_0^trdt (2) to give ln(N/(N_0))=rt, (3) ...

A condition in numerical equation solving which states that, given a space discretization, a time step bigger than some computable quantity should not be taken. The condition ...

The study of an extension of derivatives and integrals to noninteger orders. Fractional calculus is based on the definition of the fractional integral as ...

The Ricci flow equation is the evolution equation d/(dt)g_(ij)(t)=-2R_(ij) for a Riemannian metric g_(ij), where R_(ij) is the Ricci curvature tensor. Hamilton (1982) showed ...

Surface area is the area of a given surface. Roughly speaking, it is the "amount" of a surface (i.e., it is proportional to the amount of paint needed to cover it), and has ...

The sinc function sinc(x), also called the "sampling function," is a function that arises frequently in signal processing and the theory of Fourier transforms. The full name ...

The Christoffel symbols are tensor-like objects derived from a Riemannian metric g. They are used to study the geometry of the metric and appear, for example, in the geodesic ...