Inversion of Laplace transforms is a very important procedure used in solution of complex linear systems.
The function f(t)=INVLAP(F(s)) offers a simple, effective and reasonably accurate way to achieve the result. It is based on the paper:
J. Valsa and L. Brancik: Approximate Formulae for Numerical Inversion of Laplace Transforms, Int. Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Vol. 11, (1998), pp. 153-166
The transform F(s) may be any reasonable function of complex variable s^α, where α is an integer or non-integer real exponent. Thus, the function INVLAP can solve even fractional problems and invert functions F(s) containing rational, irrational or transcendental expressions.
The function does not require to compute poles nor zeroes of F(s). It is based on values of F(s) for selected complex values of the independent variable s. The resultant computational error can be held arbitrarily low at the cost of CPU time. With the today’s computers and their speed this does not present any serious limitation (see Examples).