Numerical Methods and Applications
Guri I. Marchuk
CRC Press, Mar 22, 1994 - Mathematics - 288 pages
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.
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A-stable algorithm applied approximate solution arbitrary assume asymptotic bilinear form boundary conditions boundary value problem Cauchy problems coefficients components computation consider constant Corollary corresponding D'yakonov defined denote depend derive difference schemes differential equations eigenvalue eigenvectors elasticity Equa equal Equation 2.2 Equation 3.1 Euclidean space explicit finite finite-difference scheme finite-element geometric progression grid Hilbert space identity implicit scheme inequality inner iterations iterative method Kobelkov Lemma linear Lipschitz domain Math matrix Moscow Navier-Stokes equations nodes nonlinear nonstationary norm numerical integration Numerical Methods numerical solution obtain parameters polynomial preconditioners problem 2.1 proof of Theorem prove rate of convergence reference Russian s x s s x s matrix satisfy scalar product Section simplex solution of Equation solving space H spectrum stability statement step stiff systems subspace summand symmetric term Theorem 4.1 theory tion torus triangles valid variables vector functions xn+i
Page x - Fictitious domain methods and computation of homogenized properties of composites with a periodic structure of essentially different components. In: Marchuk, Guri I.