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

A low-pass filter which is useful for smoothing data.

The partial differential equation u_t+45u^2u_x+15u_xu_(xx)+15uu_(xxx)+u_(xxxxx)=0.

A spheroidal harmonic is a special case of an ellipsoidal harmonic that satisfies the differential equation d/(dx)[(1-x^2)(dS)/(dx)]+(lambda-c^2x^2-(m^2)/(1-x^2))S=0 on the ...

The partial differential equation u_(yy)=yu_(xx).

The function psi(x)={x(1-(x^2)/(c^2))^2 for |x|<c; 0 for |x|>c (1) sometimes used in robust estimation. It has a minimum at x=-c/sqrt(5) and a maximum at x=c/sqrt(5), where ...

A random number which lies within a specified range (which can, without loss of generality, be taken as [0, 1]), with a uniform distribution.

For R[mu+nu]>0, |argp|<pi/4, and a>0, where J_nu(z) is a Bessel function of the first kind, Gamma(z) is the gamma function, and _1F_1(a;b;z) is a confluent hypergeometric ...

An optimal filter used for the removal of noise from a signal which is corrupted by the measuring process itself.

Archimedes' spiral is an Archimedean spiral with polar equation r=atheta. (1) This spiral was studied by Conon, and later by Archimedes in On Spirals about 225 BC. Archimedes ...