The stabilized march technique is extended to nonlinear two-point boundary value problems via a new Generalized Brent Method for systems of nonlinear algebraic equations. The resulting algorithms can be used to solve systems of nonlinear rst-order ordinary di erential equations under partially separated nonlinear boundary conditions economically. Numerical results which compare the nonlinear st...

In this paper we study polynomial maps of vector spaces zi → Ai1i2···is i zi1zi2zi3 · · · zis and their eigenvectors and eigenvalues. The new quantity called complanart is de ned. Complanarts determine complanarity of solution vectors of systems of polynomial equations. Evaluation of complanart is reduced to evaluation of resultants. As in linear case, the pattern of eigenvectors de nes the pha...

This paper presents a family of generalized multistep methods that evolves the numerical solution of ordinary di erential equations on con guration spaces formulated as homogeneous manifolds. Any classical multistep method may be employed as an invariant method, and the order of the invariant method is as high as in the classical setting. We present numerical results that re ect some of the pro...

We describe a MIMD parallel code to solve a general class of ordinary di erential equations, with particular emphasis on the large, sparse systems arising from space discretization of systems of parabolic partial di erential equations. The main goals of this work are sharp bounds on the accuracy of the computed solution and exibility of the software. We discuss the sources of error in solving d...

We study oscillatory behavior of a class of second-order neutral di¤erential equations relating oscillation of these equations to existence of positive solutions to associated first-order functional di¤erential inequalities. Our assumptions allow applications to di¤erential equations with both delayed and advanced arguments, and not only. New theorems complement and improve a number of results ...

We present a method to solve initial and boundary value problems using arti ial neural networks. A trial solution of the di erential equation is written as a sum of two parts. The rst part satis es the initial/boundary onditions and ontains no adjustable parameters. The se ond part is onstru ted so as not to a e t the initial/boundary onditions. This part involves a feedforward neural network, ...

The problem of simultaneous reduction of real matrices by either orthogo nal similarity or orthogonal equivalence transformations is considered Based on the Jacobi idea of minimizing the sum of squares of the complementary part of the desired form to which matrices are reduced the projected gradi ent method is used in this paper It is shown that the projected gradient of the objective function ...

The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous ows is obtained by exact integration of the modeled di erential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy e ects...

Thickeners for solid±liquid separation are still designed and controlled empirically in the mining industry. Great e€orts are being made to develop mathematical models that will change this situation. Starting from the basic principles of continuum mechanics, the authors developed a phenomenological theory of sedimentation for ̄occulated suspensions which takes the compressibility of the ̄ocs u...