Parabolic and hyperbolic contours for computing the Bromwich integral. (English) Zbl 1113.65119

Summary: Some of the most effective methods for the numerical inversion of the Laplace transform are based on the approximation of the Bromwich contour integral. The accuracy of these methods often hinges on a good choice of contour, and several such contours have been proposed in the literature. Here we analyze two recently proposed contours, namely a parabola and a hyperbola. Using a representative model problem, we determine estimates for the optimal parameters that define these contours. An application to a fractional diffusion equation is presented.


65R10 Numerical methods for integral transforms
44A10 Laplace transform
45K05 Integro-partial differential equations
35K05 Heat equation
26A33 Fractional derivatives and integrals
35A22 Transform methods (e.g., integral transforms) applied to PDEs
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