Order Stars: Theory and ApplicationsCRC Press, 1991-06-01 - 248 psl. According to Hilbert's dictum, the scaffolding should be invisible in a math ematical edifice. Less kind interpretation of this common principle of writing and presenting mathematics is that we should always strive to do it baek to-front, forever wise after the event. Nobody should be allowed to see the seams in the supposedly seamless robe or eompare authors' intentions with the outeome of their endeavour. In particular, the short pieee of prose oeea sionally labelIed 'Prefaee' or 'Forward' ought to be written after the main body of the book. And so it is, and we, the authors, can refleet (with much trepidation) on an enterprise that for us is finally over. Order stars have been originally introduced in the context of numerical solution of ordinary differential equations and, as far as many numerical an alysts are concerned, they still belong there. It is our case in this book that the seope of order stars ranges considerably wider and that the cornerstone of the order star theory is a function-theoretic interpretation of complex approximation theory. An application to numerical analysis is a matter of serendipity, not of essen ce. |
Knygos viduje
Rezultatai 1–5 iš 83
vi psl.
... stability conditions 120 6.2 The influence of boundaries on stability 129 6.3 A barrier for semi - discretizations 133 6.4 Stable full discretizations 6.5 A barrier for full discretizations 7 The diffusion equation 7.1 Methods of ...
... stability conditions 120 6.2 The influence of boundaries on stability 129 6.3 A barrier for semi - discretizations 133 6.4 Stable full discretizations 6.5 A barrier for full discretizations 7 The diffusion equation 7.1 Methods of ...
viii psl.
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ix psl.
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2 psl.
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3 psl.
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Turinys
Rational approximants to the exponential | 28 |
Aacceptability barriers | 52 |
Multistep methods | 96 |
The advection equation | 120 |
The diffusion equation | 155 |
Padé approximants | 177 |
Contractive approximation | 193 |
Open problems | 207 |
Advection equation with two space | 224 |
239 | |
Kiti leidimai - Peržiūrėti viską
Pagrindiniai terminai ir frazės
A-acceptable A-stable adjoin the origin analysis analytic function approach the origin approximants to exp asymptotic barrier Blaschke product boundary bounded A+-regions branch points Chapter coefficients collocation complex plane Consequently convergence Dahlquist defined denote error constant essential singularities essentially analytic Example explicit exponential Figure finite follows at once full discretization Hairer hence imaginary axis implies inequality integer interpolation points interval Iserles Jacobi polynomial Jeltsch left half-plane Lemma linear Math Moreover multiderivative multiplicity multistep methods Nørsett number of sectors number of zeros obeys optimal order stars ordinary differential equations p-restricted approximants Padé approximants Pm/n polynomial problem proof Proposition 2.3 prove Rainville rational approximants rational function Riemann surfaces Rm/n root condition Runge-Kutta methods scheme sectors of A+ semi-discretization singly p-restricted solution stability Theorem theory underlying unit disc V-contraction zeros and poles
Populiarios ištraukos
228 psl. - Akhiezer, NI (1965), The classical moment problem, Oliver and Boyd, Edinburgh and London. [2] Ashurst, WT and Meiron, D. (1987), "Numerical Study of Vortex Reconnection,
Šią knygą minintys šaltiniai
Dynamical Systems and Numerical Analysis, 8 tomas Andrew Stuart,A. R. Humphries Ribota peržiūra - 1998 |