Invited Lecture
Numerical inverse Laplace transform for convection-diffusion equations
Gran Sasso Science Institute, L'Aquila, Italy
Abstract
In this talk a novel contour integral method is proposed for
linear convection-diffusion equations.
The method is based on the inversion of the Laplace transform
and makes use of a contour given by an elliptic arc joined
symmetrically to two half-lines. The trapezoidal rule is the chosen
integration method for the numerical inversion of the Laplace transform,
due to its well-known fast convergence properties when applied to analytic
functions.
Error estimates are provided as well as careful indications about the
choice of several involved parameters.
The method selects the elliptic arc in the integration contour by an
algorithmic strategy based on the computation of pseudospectral
level sets of the discretized differential operator.
In this sense the method is general and can be applied to any linear
convection-diffusion equation without knowing any a priori information
about its pseudospectral geometry.
Numerical experiments performed on the Black-Scholes (1D) and Heston
(2D) equations show that the method is competitive with other contour
integral methods available in the literature.
Joint work with Maria Lopez Fernandez (Università di Roma La Sapienza) and Giancarlo Nino (University of Geneva)
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