Complex variable and regularization methods of inversion of the Laplace transform
D. D. Ang, John R. Lund, Frank Stenger · Mathematics of Computation · 1989
In this paper three methods are derived for approximating f , given its Laplace transform g on ( 0 , ∞ ) (0,\infty ) , i.e., ∫ 0 ∞ f ( t ) exp ( − s t ) d t = g ( s ) \smallint _0^\infty {f(t)\exp ( - st)\,dt = g(s)} . Assuming that g ∈ L 2 ( 0 , ∞ ) g \in {L^2}(0,\infty ) , the first method is based on a Sinc-like rational approximation of g , the second on a Sinc solution of the integral equation ∫ 0 ∞ f ( t ) exp ( − s t ) d t = g ( s ) \smallint _0^\infty {f(t)\exp ( - st)\,dt = g(s)} via standard regularization, and the third method is based on first converting ∫ 0 ∞ f ( t ) exp ( − s t ) d