This book presents new original numerical methods that have been developed to the stage of concrete algorithms and successfully applied to practical problems in mathematical physics. The book discusses new methods for solving stiff systems of ordinary differential equations, stiff elliptic problems encountered in problems of composite material mechanics, Navier-Stokes systems, and nonstationary problems with discontinuous data. These methods allow natural paralleling of algorithms and will find many applications in vector and parallel computers.
Table of Contents
Iterative Methods Based on Linearization for Nonlinear Elliptic Grid Systems, E.G. Dyakonov
How to Solve Stiff Systems of Differential Equations by Explicit Methods, V.I. Lebedev
On Numerical Methods of Solving Navier-Stokes Equations in "Velocity-Pressure" Variables, G.M. Kobelkov
Stiff Systems of Ordinary Differential Equations, R.P. Fedorenko
Convergence Rate Estimates of Finite Element Methods for Second-Order Hyperbolic Equations, A.A. Zlotnik
Fictitious Domain Methods and Computation of Homogenized Properties of Composites, N.S. Bakhvalov and A.V. Knyazev
Professor Guri Marchuk has won wide ranging international recognition for his scientific activities. He was a foreign member of the Bulgarian, Czecho-Slovak, Finnish, Indian, Polish, and French Academies of Sciences; he is a honorary doctor of the Toulouse, Carlow, Dresden, Calcutta, Oregon, and Houston Universities, among others. He was awarded a Gold Medal for Services to Science and Humanity of the Czecho-Slovak Academy of Sciences, the A. Karpinskiy Medal and Prize (Germany), and an Order of the Commander of Knights of the French Legion of Honor.