Transformada inversa de laplace: inversão algébrica via tabela e inversão numérica.

Abstract

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.