Sumudu Transform - Formal Definition

Formal Definition

The Sumudu transform of a function f(t), defined for all real numbers t ≥ 0, is the function F_s(u), defined by:

$S\{f(t)\} = F_s(u) = \int_0^\infty (1/u)e^{-t/u}f(t)\,dt.\qquad(1)$

Watugala first advocated the transform as an alternative to the standard Laplace transform, and gave it the name Sumudu transform. It was early adopted by Weerakoon, and later by others.

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