Linearization of coupled second-order nonlinear ordinary differential equations (SNODEs) is one of the open and challenging problems in the theory of differential equations. In this paper, we describe ...

SIAM Journal on Applied Mathematics, Vol. 21, No. 3 (Nov., 1971), pp. 491-494 (4 pages) Let f(t,x,x') be locally Lipschitz continuous with respect to x and x'. Using differential inequality results, ...

Partial differential equations: classification of second-order equations, separation of variables, Fourier transforms, explicit and implicit numerical schemes.

Ordinary differential equations (ODEs) are also called initial value problems because a time zero value for each first-order differential equation is needed. The following is an example of a ...

An intermediate level course in the analytical and numerical study of ordinary differential equations, with an emphasis on their applications to the real world. Exact solution methods for ordinary ...