References
- A. E. ISOTALO and W. A. WIESELQUIST, “A Method for Including External Feed in Depletion Calculations with CRAM and Implementation into ORIGEN,” Ann. Nucl. Energy, 85, 68 (2015); https://doi.org/10.1016/j.anucene.2015.04.037.
- C. MOLER and C. van LOAN, “Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later,” SIAM Rev., 45, 1, 3 (2003); https://doi.org/10.1137/S00361445024180.
- M. PUSA and J. LEPPÄNEN, “Computing the Matrix Exponential in Burnup Calculations,” Nucl. Sci. Eng., 164, 2, 140 (2010); https://doi.org/10.13182/NSE09-14.
- D. SHE, A. ZHU, and K. WANG, “Using Generalized Laguerre Polynomials to Compute the Matrix Exponential in Burnup Equations,” Nucl. Sci. Eng., 175, 3, 259 (2013); https://doi.org/10.13182/NSE12-48.
- Y. KAWAMOTO et al., “Numerical Solution of Matrix Exponential in Burn-Up Equation Using Mini-Max Polynomial Approximation,” Ann. Nucl. Energy, 80, 219 (2015); https://doi.org/10.1016/j.anucene.2015.02.015.
- D. V. WIDDER, Laplace Transform (PMS-6), Princeton University Press (2015).
- J. ABATE and P. P. VALKÓ, “Multi-Precision Laplace Transform Inversion,” Int. J. Numer. Methods Eng., 60, 5, 979 (2004); https://doi.org/10.1002/nme.995.
- A. TALBOT, “The Accurate Numerical Inversion of Laplace Transforms,” IMA J. Appl. Math., 23, 1, 97 (1979); https://doi.org/10.1093/imamat/23.1.97.
- L. N. TREFETHEN, J. A. C. WEIDEMAN, and T. SCHMELZER, “Talbot Quadratures and Rational Approximations,” BIT Num. Math., 46, 3, 653 (2006); https://doi.org/10.1007/s10543-006-0077-9.
- L. N. TREFETHEN and J. WEIDEMAN, “The Exponentially Convergent Trapezoidal Rule,” SIAM Rev., 56, 3, 385 (2014); https://doi.org/10.1137/130932132.
- B. DAVIES and B. MARTIN, “Numerical Inversion of the Laplace Transform: A Survey and Comparison of Methods,” J. Comput. Phys., 33, 1, 1 (1979); https://doi.org/10.1016/0021-9991(79)90025-1.
- A. M. COHEN, Numerical Methods for Laplace Transform Inversion, Vol. 5, Springer Science & Business Media (2007).
- J. WEIDEMAN and L. TREFETHEN, “Parabolic and Hyperbolic Contours for Computing the Bromwich Integral,” Math. Comput., 76, 259, 1341 (2007); https://doi.org/10.1090/S0025-5718-07-01945-X.
- M. PUSA, “Rational Approximations to the Matrix Exponential in Burnup Calculations,” Nucl. Sci. Eng., 169, 2, 155 (2011); https://doi.org/10.13182/NSE10-81.
- D. SHE, K. WANG, and G. YU, “Development of the Point-Depletion Code DEPTH,” Nucl. Eng. Des., 258, 235 (2013); https://doi.org/10.1016/j.nucengdes.2013.01.007.
- S. XIA et al., “The Laplace Transform Method for Solving the Burnup Equation with External Feed,” Ann. Nucl. Energy, 130, 47 (2019); https://doi.org/10.1016/j.anucene.2019.01.036.
- G. A. BAKER et al., Padé Approximants, Vol. 59, Cambridge University Press (1996).
- M. ARIOLI, B. CODENOTTI, and C. FASSINO, “The Padé Method for Computing the Matrix Exponential,” Linear Algebra Appl., 240, 111 (1996); https://doi.org/10.1016/0024-3795(94)00190-1.
- N. J. HIGHAM, “Evaluating Padé Approximants of the Matrix Logarithm,” SIAM J. Matrix Anal. Appl., 22, 4, 1126 (2001); https://doi.org/10.1137/S0895479800368688.
- N. J. HIGHAM, “The Scaling and Squaring Method for the Matrix Exponential Revisited,” SIAM J. Matrix Anal. Appl., 26, 4, 1179 (2005); https://doi.org/10.1137/04061101X.
- K. SINGHAL and J. VLACH, “Computation of Time Domain Response by Numerical Inversion of the Laplace Transform,” J. Franklin Inst., 299, 2, 109 (1975); https://doi.org/10.1016/0016-0032(75)90133-7.
- R. PIESSENS, “On a Numerical Method for the Calculation of Transient Responses,” J. Franklin Inst., 292, 1, 57 (1971); https://doi.org/10.1016/0016-0032(71)90041-X.
- V. ZAKIAN, “Properties of IMN and JMN Approximants and Applications to Numerical Inversion of Laplace Transforms and Initial Value Problems,” J. Math. Anal. Appl., 50, 1, 191 (1975); https://doi.org/10.1016/0022-247X(75)90048-7.
- D. CALVETTI, E. GALLOPOULOS, and L. REICHEL, “Incomplete Partial Fractions for Parallel Evaluation of Rational Matrix Functions,” J. Comput. Appl. Math., 59, 3, 349 (1995); https://doi.org/10.1016/0377-0427(94)00037-2.
- A. ISOTALO and M. PUSA, “Improving the Accuracy of the Chebyshev Rational Approximation Method Using Substeps,” Nucl. Sci. Eng., 183, 1, 65 (2016); https://doi.org/10.13182/NSE15-67.
- J. H. MATHEWS et al., Numerical Methods Using MATLAB, 4th ed., Vol. 4, pp. 242–247, Pearson Prentice Hall, Upper Saddle River, New Jersey, 2004.
- E. HOROWITZ, “Algorithms for Partial Fraction Decomposition and Rational Function Integration,” Proc. 2nd ACM Symp. on Symbolic and Algebraic Manipulation, pp., 441–457, Association for Computing Machinery (1971).
- M. PUSA, “Higher-Order Chebyshev Rational Approximation Method and Application to Burnup Equations,” Nucl. Sci. Eng., 182, 3, 297 (2016); https://doi.org/10.13182/NSE15-26.
- I. GAULD, “ORIGEN-S: Depletion Module to Calculate Neutron Activation, Actinide Transmutation, Fission Product Generation, and Radiation Source Terms,” ORNL/TM-2005/39, Oak Ridge National Laboratory (2011).
- A. ISOTALO and P. AARNIO, “Comparison of Depletion Algorithms for Large Systems of Nuclides,” Ann. Nucl. Energy, 38, 2–3, 261 (2011); https://doi.org/10.1016/j.anucene.2010.10.019.
- M. PUSA, “Accuracy Considerations for Chebyshev Rational Approximation Method (CRAM) in Burnup Calculations,” Proc. Int. Conf. Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2013), pp. 973–984, Sun Valley, Idaho, May 5-9 (2013).