ILT {TCIU}

numerical method to compute inverse of Laplace Transform

Description

a function that numerically computes the inverse of Laplace Transform

Usage

ILT(
  FUNCT,
  t,
  nterms = 31L,
  m = 1,
  gamma = 0.5,
  fail_val = complex(0),
  msg = TRUE
)

Arguments

FUNCT

function object F(z), typically a Laplace Transform of a function f(t)

t

time domain value to evaluate the ILT(F)(t)

nterms

number of terms to use in the numerical inversion (odd number). The default is 31L.

m

width of the contour path in C; too small values may lead to singularities on the negative x-axis; too large valued may lead to numerical instability for large positive x-axis. The default is 1.

gamma

value on the positive x-axis for the vertical line representing the contour. The default is 0.5

fail_val

value to return in event of failure to converge

msg

Boolean to show/hide warnings. The default is TRUE.

Details

This function first uses full optimum contour path to do inverse Laplace Transform. However, if this method fails, the function will automatically change to the method of using Bromwich contour path to do inverse Laplace Transform

Value

a real value computed from inverse Laplace Transform

Author(s)

SOCR team <http://socr.umich.edu/people/>

Examples

# analytic form of Laplace transform of f(t) = t
F = function(z) { 1/(z^2) }
# do inverse Laplace transform on t = 0.2
ILT(F, t = 0.2)
# the result is equal to t = 0.2