GALDINO, K. E.; http://lattes.cnpq.br/0657038729605079; GALDINO, Kátia Elizabete.
Resumo:
A differential equation is a relation involving terms which are derivatives of an
unknown function / . The Laplace transform of a differential equation is an equation
in the complex domain without derivatives. The new equation, free of derivatives, may
be easier to solve then the original equation, but the solution obtained is the Laplace
transform of / instead o f / . To obtain / the inverse Laplace transform must be applied.
The Laplace transform and its inverse are both defined as an integral in the complex
domain.
Having a Laplace transform of a function / , Cf , its inverse C~lf is obtained by
a) searching a table of inverse Laplace transforms, or
b) decomposing Cf into simple forms whose inverses are in a table, or
c) applying the definition of the inverse transform and analytically integrate the
resulting expression, or
d) solving numerically the defining integral of the inverse in order to get values of
/ i n discrete points of the domain if the previous methods fail.
This work surveys recent numerical Laplace transform inversion methods, presents
some experimental results, and points out some difficulties to implement easy to use
routines for this inversion.