Local linearization method: Difference between revisions

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* Biscay R. et al. (1996) reformulate the strong LL method for SDEs.<ref name=″:20″> Biscay, R., Jimenez, J. C., Riera, J. J., & Valdes, P. A. (1996). Local linearization method for the numerical solution of stochastic differential equations. Annals of the Institute of Statistical Mathematics, 48(4), 631-644.[[doi:10.1007/BF00052324|<small>doi:10.1007/BF00052324</small>]] </ref>

* Shoji I. and Ozaki T. (1997) reformulate the weak LL method for SDEs.<ref name=″:21″> Shoji, I., & Ozaki, T. (1997). Comparative study of estimation methods for continuous time stochastic processes. Journal of time series analysis, 18(5), 485-506.[[doi:10.1111/1467-9892.00064|<small>doi: 10.1111/1467-9892.00064</small>]]</ref>

* Hochbruck M. et al. (1998) introduce the LL scheme for ODEs based on Krylov subspace approximation. <ref name="″:22″">Hochbruck, M., Lubich, C., & Selhofer, H. (1998). Exponential integrators for large systems of differential equations. SIAM JournalJ. on ScientificScient. Computing,Comput. 19(5), 1552-1574.[[doi:10.1137/S1064827595295337|<small>doi:10.1137/S1064827595295337</small>]]</ref>

* Jimenez J.C. (2002) introduces the LL scheme for ODEs and SDEs based on rational Padé approximation. <ref name=″:23″>Jimenez, J. C. (2002). A simple algebraic expression to evaluate the local linearization schemes for stochastic differential equations. Applied Mathematics Letters, 15(6), 775-780.[[doi:10.1016/S0893-9659(02)00041-1|<small>doi:10.1016/S0893-9659(02)00041-1</small>]]</ref>

* Carbonell F.M. et al. (2005) introduce the LL method for RDEs. <ref name=″:24″>Carbonell, F., Jimenez, J. C., Biscay, R. J., & De La Cruz, H. (2005). The local linearization method for numerical integration of random differential equations. BIT Numerical Mathematics, 45(1), 1-14. [https://doi.org/10.1007%2FS10543-005-2645-9 doi:10.1007/s10543-005-2645-9]</ref>