Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014, Article ID 812137, 12 pages
http://dx.doi.org/10.1155/2014/812137
Research Article

Iterative Splitting Methods for Integrodifferential Equations: Theory and Applications

Department of Physics, Ernst-Moritz-Arndt University of Greifswald, Domstraße 14, 17487 Greifswald, Germany

Received 30 May 2014; Revised 5 August 2014; Accepted 5 August 2014; Published 24 August 2014

Academic Editor: Giuseppe Marino

Copyright © 2014 Jürgen Geiser. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Geiser, “An iterative splitting approach for linear integro-differential equations,” Applied Mathematics Letters, vol. 26, no. 11, pp. 1048–1052, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. J. Geiser, “Multiscale splitting method for the Boltzmann-Poisson equation: application to the dynamics of electrons,” International Journal of Differential Equations, vol. 2014, Article ID 178625, 8 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  3. S. Blanes, F. Casas, and A. Murua, “Error analysis of splitting methods for the time dependent Schrödinger equation,” SIAM Journal on Scientific Computing, vol. 33, no. 4, pp. 1525–1548, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. R. Bhatia, Matrix Analysis, vol. 169 of Graduate Texts in Mathematics, Springer, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  5. G. Strang, “On the construction and comparison of difference schemes,” SIAM Journal on Numerical Analysis, vol. 5, pp. 506–517, 1968. View at Publisher · View at Google Scholar · View at MathSciNet
  6. J. Verwer and B. Sportisse, “A note on operator splitting in a stiff linear case,” MAS Report R9830, 1998. View at Google Scholar
  7. Z. Zlatev, Computer Treatment of Large Air Pollution Models, Kluwer Academic, New York, NY, USA, 1995.
  8. J. F. Kanney, C. T. Miller, and C. T. Kelley, “Convergence of iterative split-operator approaches for approximating nonlinear reactive problems,” Advances in Water Resources, vol. 26, no. 3, pp. 247–261, 2003. View at Publisher · View at Google Scholar · View at Scopus
  9. E. J. Dean, R. Glowinski, and J. L. Lions, “An operator splitting approach to multilevel methods,” Applied Mathematics Letters, vol. 15, no. 4, pp. 505–511, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. J. Geiser, Iterative Splitting Methods for Differential Equations, CRC Press, Chapman & Hall, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  11. J. Geiser, “Computing exponential for iterative splitting methods: algorithms and applications,” Journal of Applied Mathematics, vol. 2011, Article ID 193781, 27 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. S. H. Cheng, N. J. Higham, C. S. Kenney, and A. J. Laub, “Approximating the logarithm of a matrix to specified accuracy,” SIAM Journal on Matrix Analysis & Applications, vol. 22, no. 4, pp. 1112–1125, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. E. D. Denman and J. Beavers, “The matrix sign function and computations in systems,” Applied Mathematics and Computation, vol. 2, no. 1, pp. 63–94, 1976. View at Google Scholar · View at MathSciNet · View at Scopus