an:00177350
Zbl 0773.65090
Ryabov, V. M.
Quadrature formulas of highest degree of precision for inversion of the Laplace transformation
EN
Optimal recovery, Proc. 2nd Int. Symp. Optim. Control, Varna/Bulg. 1989, 273-280 (1992).
1992
a
65R10 65D32 65R30 41A55 44A10
Laplace transform inversion; Riemann-Mellin integral; quadrature formulas; highest degree of precision; convergence; error estimates
[For the entire collection see Zbl 0755.00006.]
The inversion problem for the Laplace transformation is a problem of finding the solution of the equation \(\int_ 0^ \infty e^{- pt}f(t)dt=F(p)\), where \(F(p)\) is a given mapping and \(f(t)\) is the wanted original function. The author considers the inversion formula for the Laplace transformation in the form of the Riemann-Mellin integral
\[
f(t)={1\over 2\pi i}\int_{c-i\infty}^{c+i\infty}e^{pt}F(p) dp,\quad c>0, \tag{1}
\]
and discusses the construction of quadrature formulas for computation of the integral in (1). Several results about quadrature formulas of highest degree of precision are presented and their rate of convergence and error estimates are given.
G.Grozev (Montreal)
Zbl 0755.00006