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Numerical Inversion of the Laplace Transform by Use of Jacobi Polynomials
Max K. Miller and W. T. Guy, Jr.
SIAM Journal on Numerical Analysis
Vol. 3, No. 4 (Dec., 1966), pp. 624-635
Published by: Society for Industrial and Applied Mathematics
Stable URL: http://www.jstor.org/stable/2949575
Page Count: 12
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Functional values of a function f are determined from the values F(s) of its Laplace transform at discrete points of s. Evaluation of F(s) at points given by s = (β + 1 + k)δ, k = 0, 1, ⋯, determine coefficients in an infinite series expansion of f(t) in terms of Jacobi polynomials. The values of β and δ determine the position along the real s-axis at which F(s) is evaluated. An approximation to f(t) is given by using a finite number of terms of the infinite series expansion of f(t). Numerical examples are given and results are compared with some known numerical methods for approximating f(t).
SIAM Journal on Numerical Analysis © 1966 Society for Industrial and Applied Mathematics