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A method of inversion of the Laplace transform. (English) Zbl 0753.65097
Let \(F\) be the Laplace transform of \(f(t)\) and \(F_ j=F(p_ 0+jh)\) with \(h>0\) and suitable large \(p_ 0\). The author determines an approximation \(f_ k(t)=\sum^ k_{i=1}S_ ie^{-m_ it}\) of \(f(t)\) by means of the overdetermined system \(F_ j=\sum^ k_{i=1}S_ i/(p_ 0+jh+m_ i)\), \(j=0,1,\dots,n\), \(n>2k\). The unknowns \(m_ i\) can be determined by means of a polynomial equation of order \(k\), so that the nonlinear system turns into a linear one for the \(S_ i\).
Reviewer: L.Berg (Rostock)
MSC:
65R10 Numerical methods for integral transforms
44A10 Laplace transform
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References:
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