Asymptotic Analysis of Differential EquationsWorld Scientific, 2010 - 405 strán (strany) The book gives the practical means of finding asymptotic solutions to differential equations, and relates WKB methods, integral solutions, Kruskal-Newton diagrams, and boundary layer theory to one another. The construction of integral solutions and the use of analytic continuation are used in conjunction with the asymptotic analysis, to show the interrelatedness of these methods. Some of the functions of classical analysis are used as examples, to provide an introduction to their analytic and asymptotic properties, and to give derivations of some of the important identities satisfied by them. The emphasis is on the various techniques of analysis: obtaining asymptotic limits, connecting different asymptotic solutions, and obtaining integral representation. |
Obsah
1 Dominant Balance | 1 |
2 Exact Solutions | 15 |
3 Complex Variables | 31 |
4 Local Approximate Solutions | 43 |
5 PhaseIntegral Methods I | 73 |
6 PerturbationTheory | 105 |
7 Asymptotic Evaluation of Integrals | 117 |
8 The Euler Gamma Function | 133 |
13 Bessel | 247 |
14 Weber and Hermite | 271 |
15 Whittaker and Watson | 285 |
16 Inhomogeneous Differential Equations | 299 |
17 The Riemann Zeta Function | 327 |
18 Boundary Layer Problems | 343 |
Appendix A LagrangesTheorem | 393 |
Appendix B Integral Solution for Eq 18129 | 395 |
9 Integral Solutions | 151 |
10 Expansion in Basis Functions | 165 |
11 Airy | 195 |
12 PhaseIntegral Methods II | 213 |
| 397 | |
| 401 | |
Iné vydania - Zobraziť všetky
Asymptotic Analysis Of Differential Equations (Revised Edition) Roscoe B White Obmedzený náhľad - 2010 |
Časté výrazy a frázy
Ai(z Airy function analytic continuation anti-Stokes lines approximation asymptotic behavior asymptotic expansion asymptotic form asymptotic series Bessel function boundary conditions coefficients contribution convergence defined diagram for Eq differential equation dominant balance Dp(z eigenvalues end point Euler evaluation Fourier-Laplace Gamma function given giving half plane homogeneous equation Im(t infinity inhomogeneous integral representation integral solution integrand integration contour Integration path irregular singular point Kruskal-Newton diagram large positive layer leading order matching Mellin representation number of terms numerical integration obtained order uniform solution orthogonal parabolic cylinder function perturbation phase pole polynomial positive real Re(t real axis regular singular regular singular point saddle point showing shown in Fig steepest descent Stokes constant Stokes diagram Stokes line Stokes plot subdominant subdominant solution Substituting theory tion turning points values variable wave wavelet WKBJ write Wronskian