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We describe a FORTRAN implementation, and some related problems, of Talbot's method which numerically solves the inversion problem of almost arbitrary Laplace transforms by means of special contour integration ... The basic idea is to take into account computer precision to derive a special contour where integration will be carried out. ... ACKNOWLEDGMENT We would like to acknowledge the help and encouragement given by James N. Lyness on a preliminary version of this paper. ...doi:10.1145/78928.78932 fatcat:sb2uayx7zbcpzb4moryifbmbmm
Journal of the Atmospheric Sciences
Rizzardi, 1990: Algorithm 682: Talbot’s method for the Laplace inversion. ACM Trans. Math. Software, 16, 158 168. Nicholls, M. E., and R. A. Pielke, 1994a: Thermal compression waves. ... This method was used rather than Talbot’s method to avoid the classification and location of the singularities. REFERENCES Bannon, P. R., 1995: Hydrostatic adjustment: Lamb’s problem. J. Atmos. ...
For the numerical inversion of Laplace transforms we suggest to use multi-precision computing with the level of precision determined by the algorithm. We present two such procedures. ... The fixed Talbot (FT) method is based on the deformation of the contour of the Bromwich inversion integral and requires complex arithmetic. ... There are over 100 algorithms available for the numerical inversion of Laplace transforms. Three important comparative studies of methods have been published. ...doi:10.1002/nme.995 fatcat:afpls3uqqraklmpwm5tmhfqnwm
The classical Talbot method for the computation of the inverse Laplace transform is improved for the case where the transform is analytic in the complex plane except for the negative real axis. ... It is shown that even when the transform has singularities off the negative real axis, rapid convergence can still be achieved in many cases. ... Conclusions A truncated version of Talbot's famous contour for numerical Laplace transform inversion was analyzed. ...arXiv:1304.2505v3 fatcat:nmnjeyp6lvay5gla57tdcwgqqi
A semi-analytic approach is developed which allows us to consider the behaviour of the shape of the spectral cut-off and the variation of that cut-off with the particle pitch angle. ... We investigate the acceleration and simultaneous radiative losses of electrons in the vicinity of relativistic shocks. ... to proceed with this problem and it is more straightforward to define the cut-off in terms of spectral steepening of the Laplace-transformed spectrum. ...doi:10.1111/j.1365-2966.2007.11800.x fatcat:2v7jni5ikjgwnp6ej5dots4u3q
Kwok and Barthez  write that "The inversion of the Laplace transform is well known to be an ill-conditioned problem. ... For example, the method of Bellman, Kalaba and Lockett , which is based on approximately converting the inversion problem to that of solving a system of linear algebraic equations, is notorious for ... Algorithm 662 is a variant of the Weeks  method; and Algorithm 682 is Talbot's  method. ...doi:10.1007/bf01158520 fatcat:wlumnr6jxrgaxkwxbknqftwss4
Rizzardi, 1990: Algorithm 682: Talbot’s method for the Laplace inversion. ACM Trans. Math. Software, 16, 158 168. Nicholls, M. E., and R. A. Pielke, 1994a: Thermal compression waves. ... Numerical inversion of all of the transforms was done using Talbot’s method (Murli and Rizzardi 1990) except for those terms when the inverse could be obtained by inspection. ...doi:10.1175/1520-0469(2003)060<0339:haina>2.0.co;2 fatcat:ul627sq5azcovhkcqzwrw2yn2q