Higher order discretization methods for y″ = f(x, y, y′)

Mixed Collocation Methods for Y" = F(x,y)

-Y, Y loss in leukemia

Note Loss of the Y chromosome from individual metaphases is common in metaphase cells from both PHAstimulated lymphocytes and spontaneously dividing bone marrow cells. The frequency of Y loss is greater in older men, and the size of the 45,X,-Y cell population probably increases gradually with advancing age. (In females, a corollary loss of one X chromosome also occurs with advancing age.) This...

Embedded explicit Runge-Kutta type methods for directly solving special third order differential equations y'''=f(x, y)

In this paper three pairs of embedded Runge–Kutta type methods for directly solving special third order ordinary differential equations (ODEs) of the form denoted as RKD methods are presented. The first is the RKD4(3) pair which is third order embedded in fourth-order method has the property first same as last (FSAL) whereby the last row of the coefficient matrix is equal to the vector output. ...

local FMm,n-diffeomorphism f: Y → Y.

Let r, s, q,m, n ∈ N be such that s ≥ r ≤ q. Let Y be a fibered manifold with m-dimensional basis and n-dimensional fibers. All natural affinors on (J(Y,R)0) are classified. It is deduced that there is no natural generalized connection on (J(Y,R)0). Similar problems with (J(Y,R)0) instead of (J(Y,R)0) are solved.

Complete Characterization of Multistep Methods with an Interval of Periodicity for Solving y"=f[x,y)

Linear multistep methods for the second order differential equation y" = 2 — X y, X real, are said to have an interval of periodicity if for a fixed X. and a stepsize sufficiently small the numerical solution neither explodes nor decays. We give a very simple necessary and sufficient condition under which a linear multistep method has an interval of periodicity. This condition is then applied t...