A modification of the weeks method for numerical inversion of the Laplace transform
Mathematics of Computation
ACM Transactions on Mathematical Software (TOMS)
Numerical Inversion of Laplace Transforms Using Laguerre Functions
Journal of the ACM (JACM)
Algorithms for Parameter Selection in the Weeks Method for Inverting the Laplace Transform
SIAM Journal on Scientific Computing
Algorithm 368: Numerical inversion of Laplace transforms [D5]
Communications of the ACM
Python for Scientific Computing
Computing in Science and Engineering
Numerical Methods for Laplace Transform Inversion
Numerical Methods for Laplace Transform Inversion
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A boundary element method (BEM) simulation is used to compare the efficiency of numerical inverse Laplace transform strategies, considering general requirements of Laplace-space numerical approaches. The two-dimensional BEM solution is used to solve the Laplace-transformed diffusion equation, producing a time-domain solution after a numerical Laplace transform inversion. Motivated by the needs of numerical methods posed in Laplace-transformed space, we compare five inverse Laplace transform algorithms and discuss implementation techniques to minimize the number of Laplace-space function evaluations. We investigate the ability to calculate a sequence of time domain values using the fewest Laplace-space model evaluations. We find Fourier-series based inversion algorithms work for common time behaviors, are the most robust with respect to free parameters, and allow for straightforward image function evaluation re-use across at least a log cycle of time.