Over the past fifteen years two new techniques have yielded extremely important
contributions toward the numerical solution of nonlinear systems of equations. This book …

This book was intended as an introduction to the topic of numerical continuation which
would be accessible to a readership of widely varying mathematical backgrounds. Realizing …

Pattern formation in physical systems is one of the major research frontiers of mathematics.
A central theme of this book is that many instances of pattern formation can be understood …

Motivated by processes occurring during sequestration in an underground saline aquifer, we
examine two-dimensional convection in a finite-depth porous medium induced by a solute …

A full 3-D numerical study is reported on natural convection of air in six heated-from-below
parallelepipedic enclosures. A supercritical Rayleigh number (Ra= 8× 10 3), was used in …

Numerical simulations are carried out to determine the steady-state convective modes in a
rectangular porous cavity heated from below. The property of multiplicity of solutions for a …

Sequential transitions of the thermal convection in a square cavity heated from below are
investigated up to the time periodic state by numerical simulation. The flow field is assumed …

A new class of homotopy continuation methods is developed suitable for globalizing quasi-
Newton methods for large sparse nonlinear systems of equations. The new continuation …

Techniques of bifurcation theory are used to study the porous-medium analogue of the
classical Rayleigh-Bénard problem, Lapwood convection in a two-dimensional saturated …

In this paper, simulations of two-dimensional (2D) double-diffusive convection in an inclined
cavity were conducted using a high-accuracy numerical method. The cavity is gradually …