steepest-descent%20paths
(0.003 seconds)
1—10 of 152 matching pages
1: 5.21 Methods of Computation
…
►Another approach is to apply numerical quadrature (§3.5) to the integral (5.9.2), using paths of steepest descent for the contour.
…
2: 9.17 Methods of Computation
…
►As described in §3.7(ii), to ensure stability the integration path must be chosen in such a way that as we proceed along it the wanted solution grows at least as fast as all other solutions of the differential equation.
…
►In the first method the integration path for the contour integral (9.5.4) is deformed to coincide with paths of steepest descent (§2.4(iv)).
…
3: 2.4 Contour Integrals
…
►Let denote the path for the contour integral
…
►Additionally, it may be advantageous to arrange that is constant on the path: this will usually lead to greater regions of validity and sharper error bounds.
Paths on which is constant are also the ones on which decreases most rapidly.
For this reason the name method of steepest
descents is often used.
However, for the purpose of simply deriving the asymptotic expansions the use of steepest descent paths is not essential.
…
4: 3.5 Quadrature
…
►For these cases the integration path may need to be deformed; see §3.5(ix).
…
►
§3.5(ix) Other Contour Integrals
… ►For example, steepest descent paths can be used; see §2.4(iv). … ►The steepest descent path is given by , or in polar coordinates we have . … ►A special case is the rule for Hilbert transforms (§1.14(v)): …5: Bibliography T
…
►
Steepest descent paths for integrals defining the modified Bessel functions of imaginary order.
Methods Appl. Anal. 1 (1), pp. 14–24.
…
6: Bibliography P
…
►
Exactification of the method of steepest descents: The Bessel functions of large order and argument.
Proc. Roy. Soc. London Ser. A 460, pp. 2737–2759.
…
►
Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
…
7: Bibliography B
…
►
Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
…
►
Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
…
►
Error bounds for the method of steepest descents.
Proc. Roy. Soc. London Ser. A 440, pp. 493–518.
►
Gamma function asymptotics by an extension of the method of steepest descents.
Proc. Roy. Soc. London Ser. A 447, pp. 609–630.
►
Approximations for the late coefficients in asymptotic expansions arising in the method of steepest descents.
Methods Appl. Anal. 2 (4), pp. 475–489.
…
8: 36.5 Stokes Sets
…
►where denotes a real critical point (36.4.1) or (36.4.2), and denotes a critical point with complex or , connected with by a steepest-descent path (that is, a path where ) in complex or space.
…
►
36.5.4
…
►
36.5.7
…
9: Bibliography C
…
►
Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
…
►
An extension of the method of steepest descents.
Proc. Cambridge Philos. Soc. 53, pp. 599–611.
…
►
Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
…
►
Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
…
10: 13.20 Uniform Asymptotic Approximations for Large
…