Solving point burnup equations by Magnus method |
Cai, Yun
(Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institute of China)
Peng, Xingjie (Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institute of China) Li, Qing (Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institute of China) Du, Lin (Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institute of China) Yang, Lingfang (Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institute of China) |
1 | H.A. Ashi, L.J. Cummings, P.C. Matthews, Comparison of methods for evaluating functions of a matrix exponential, Appl. Numer. Math. 59 (2009) 468-486. DOI |
2 | H. Bateman, The solution of a system of differential equations occurring in the theory of radioactive transformations, Proc. Camb. Phil. Soc. 15 (1910) 423-427. |
3 | A.G. Croff, A User's Manual for the ORIGEN2 Computer Code, Oak Ridge National Laboratory, 1980. ORNL/TM-7175. |
4 | A. Yamamoto, M. Tatsumi, N. Sugimura, et al., Numerical solution of stiff burnup equation with short half lived nuclides by the Krylov subspace method, J. Nucl. Sci. Technol. 44 (2) (2007) 147-154. DOI |
5 | M. Pusa, Rational approximations to the matrix exponential in burnup calculations, Nucl. Sci. Eng. 169 (2) (2011) 155-167. DOI |
6 | D. She, K. Wang, G.L. Yu, Development of the point-depletion code DEPTH, Nucl. Eng. Des. 258 (2013a) 235-240. DOI |
7 | S. Blanes, et al., The Magnus expansion and some of its applications, Phys. Rep. 470 (2009) 151-238. DOI |
8 | F. Casas, A. Iserles, Explicit Magnus expansions for nonlinear equations, J. Phys. Math. Gen. 39 (2006) 5445-5461. DOI |
9 | D. She, A. Zhu, K. Wang, Using generalized Laguerre polynomials to compute the matrix exponential in burnup equations, Nucl. Sci. Eng. 175 (3) (2013b) 259-265. DOI |
10 | Y. Kawamoto, G. Chiba, M. Tsuji, et al., Numerical solution of matrix exponential in burn-up equation using mini-max polynomial approximation, Ann. Nucl. Energy 80 (2015) 219-224. DOI |
11 | S. Blanes, P.C. Moan, Fourth- and sixth-order commutator-free Magnus integrators for linear and non-linear dynamical systems, Appl. Numer. Math. 56 (2006) 1519-1537. DOI |
12 | A.E. Isotalo, P.A. Aarnio, Comparison of depletion algorithms for large systems of nuclides, Ann. Nucl. Energy 38 (2) (2011) 261-268. DOI |
![]() |