Numerical Analysis and Partial Differential Equations: Contemporary State of Numerical AnalysisThese survey articles, as any of their kind, have the primary objective of accounting in a summary fashion for the state of the fields which they cover, as determined by contributing developments at various times and in many places. Considering the sustained growth of mathematics itself, as well as the intensive use of an ever-increasing number of its branches in diversified applied contexts, the availability of such surveys in selected areas is believed to fill a real need. The present articles are therefore aimed not so much at research specialists, actively contributing to the subjects discussed, as they are aimed at a broader, mathematically literate audience, looking for contemporary information on the important problems and results in these disciplines, whether it be for use in classroom and seminar, or for the sake of possible application to problems in other fields of science and engineering, or simply for reasons of personal interest. The selection of the areas surveyed, as well as their coverage, was further guided by giving first consideration to developments of whose current state no comprehensive picture could be obtained by going only to the readily accessible literature in familiar languages. It is a unique distinction of the mathematical community to have never been taken in by the myth, now generally shattered, that Russian science merely followed the lead of the West-at a respectful distance. Mathematicians remained aware of the vigorous development during the postwar years of research in their field also in the Communist countries, and they knew of the steady stream of important results which they produced. |
Contents
Contemporary State of Numerical Analysis 3 | 3 |
AREAS OF NUMERICAL ANALYSIS 7 | 7 |
AN OLDER SOVIET VIEW OF NUMERICAL ANALYSIS 8 | 8 |
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Acad Akad algorithm Amer analytic applied Banach space BESM boundary value bounded domain C₁ Cauchy data Cauchy problem Čebyšev compact complete constant coefficients convergence cyclic single-step defined dense derivatives difference equations differential operator digital computers Dirichlet drum computers eigenvalue problem eigenvalues elements elliptic equations elliptic operator elliptic systems équations finite formulas Fourier fundamental solution Gaussian elimination given Gp(t heat equation Hilbert space Hörmander interpolation iteration Kantorovič Krylov Laplace equation Laplace transform linear operator linear systems machines Math mathematical mathematicians matrix microsecond nonnegative norm numerical analysis obtain partial differential equations Pn(x polynomial Proc properties Pure Appl Riesz Russian S₁ satisfies scalar semigroups solve Soviet Stiefel testing space theory tions unique value problem variables vector weak solution zero