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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
Stable URL: http://www.jstor.org/stable/2949575
Page Count: 12
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Numerical Inversion of the Laplace Transform by Use of Jacobi Polynomials
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Abstract

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).

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