Inverse Laplace Transform

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Description

Functionals that numerically invert a Laplace Transform.

Usage

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iv.opC(L.FUN, t, nterms = 31L, m = 1, fail.val = NA)

iv.opChalf(L.FUN, t, nterms = 16L, m = 1, fail.val = NA)

iv.BrC(L.FUN, t, nterms = 1000L, gamma = 1)

Arguments

L.FUN

the Laplace-Transformed function

t

standard (time) domain function at which to evaluate

nterms

number of terms to use in the numerical inversion (odd number safest for iv.opC, even for iv.opChalf)

m

see opC.r documentation

fail.val

value to return in event of failure to converge

gamma

the Bromwich contour is a straight line and intersects the real axis at γ

Details

Optimum contour based on:

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

Functions

  • iv.opC: inversion using the full optimum contour

  • iv.opChalf: for functions which are symmetric about the real axis, it is sufficient to use half the optimum contour and half the number of subdivisions (nterms)

  • iv.BrC: inversion using the Bromwich contour (the definition, but very unstable for numerical evaluation - not recommended)

Examples

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tvals <- seq(-pi/2, pi/2, length.out = 7)
sinvals <- vapply(tvals, iv.opC, complex(1), L.FUN = L.sin)
plot(tvals, Re(sinvals), type = "l")