Optimum Contour

Description

The optimum contour with polar co-ordinates (r as a function of φ) and complex length increment with φ (Evans and Chung, 2000)

Usage

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opC.r(phi, m = 1, t = 5)

opC.ds_dphi(phi, m = 1, t = 5)

Arguments

phi

φ value

m

width of the contour - too small and get too close to singularities on negative x-axis, too large and encounter instability for large positive x

t

standard (time) domain variable, also affects contour width

Details

if t is set as zero, it is changed to 5 (avoids dividing by 0)

Evans & Chung, 2000: Laplace transform inversions using optimal contours in the complex plane International Journal of Computer Mathematics v73 pp531-543.

Functions

  • opC.r: r

  • opC.ds_dphi: ds/dφ