This work forms part of a thesis presented in Grenoble in March 1972. Improvements made to the Dubner and Abate algorithm for numerical inversion of the Laplace transform [1] have led to results which compare favorably with theirs and those of Bellmann [2], and Stehfest [3]. The Dubner method leads to the approximation formula: ƒ(t) = 2eat/T[1/2Re{F(a)} + ∑∞k-1 Re{F(a + ik&pgr;/T)}cos(k&pgr;t/T)], (1) where F(s) is the Laplace transform of ƒ(t) and a is positive and greater than the real parts of the singularities of ƒ(t).
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