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Numerical inversion of Laplace transform based on Bernstein operational matrix
Author(s) -
Rani Dimple,
Mishra Vinod,
Cattani Carlo
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5188
Subject(s) - mathematics , bernstein polynomial , laplace transform , inverse laplace transform , orthonormal basis , laplace transform applied to differential equations , two sided laplace transform , inverse , mathematical analysis , inversion (geology) , post's inversion formula , numerical integration , orthogonal polynomials , matrix (chemical analysis) , condition number , green's function for the three variable laplace equation , fourier transform , eigenvalues and eigenvectors , fourier analysis , geometry , fractional fourier transform , paleontology , materials science , structural basin , composite material , biology , physics , quantum mechanics
This paper provides a technique to investigate the inverse Laplace transform by using orthonormal Bernstein operational matrix of integration. The proposed method is based on replacing the unknown function through a truncated series of Bernstein basis polynomials and the coefficients of the expansion are obtained using the operational matrix of integration. This is an alternative procedure to find the inversion of Laplace transform with few terms of Bernstein polynomials. Numerical tests on various functions have been performed to check the applicability and efficiency of the technique. The root mean square error between exact and numerical results is computed, which shows that the method produces the satisfactory results. A rough upper bound for errors is also estimated.