The method of lines for hyperbolic stochastic functional partial differential equations

Monika Wrzosek; Maria Ziemlańska

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 2, page 323-339
  • ISSN: 0011-4642

Abstract

top
We apply an approximation by means of the method of lines for hyperbolic stochastic functional partial differential equations driven by one-dimensional Brownian motion. We study the stability with respect to small L 2 -perturbations.

How to cite

top

Wrzosek, Monika, and Ziemlańska, Maria. "The method of lines for hyperbolic stochastic functional partial differential equations." Czechoslovak Mathematical Journal 68.2 (2018): 323-339. <http://eudml.org/doc/294679>.

@article{Wrzosek2018,
abstract = {We apply an approximation by means of the method of lines for hyperbolic stochastic functional partial differential equations driven by one-dimensional Brownian motion. We study the stability with respect to small $L^2$-perturbations.},
author = {Wrzosek, Monika, Ziemlańska, Maria},
journal = {Czechoslovak Mathematical Journal},
keywords = {stochastic partial differential equation; stability of the method of lines; white noise; Volterra stochastic equation},
language = {eng},
number = {2},
pages = {323-339},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The method of lines for hyperbolic stochastic functional partial differential equations},
url = {http://eudml.org/doc/294679},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Wrzosek, Monika
AU - Ziemlańska, Maria
TI - The method of lines for hyperbolic stochastic functional partial differential equations
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 2
SP - 323
EP - 339
AB - We apply an approximation by means of the method of lines for hyperbolic stochastic functional partial differential equations driven by one-dimensional Brownian motion. We study the stability with respect to small $L^2$-perturbations.
LA - eng
KW - stochastic partial differential equation; stability of the method of lines; white noise; Volterra stochastic equation
UR - http://eudml.org/doc/294679
ER -

References

top
  1. Ashyralyev, A., Koksal, M. E., Agarwal, R. P., 10.1016/j.mcm.2010.03.012, Math. Comput. Modelling 52 (2010), 409-424. (2010) Zbl1201.65150MR2645953DOI10.1016/j.mcm.2010.03.012
  2. Ashyralyev, A., Yurtsever, H. A., 10.1016/j.camwa.2006.08.017, Comput. Math. Appl. 52 (2006), 259-268. (2006) Zbl1137.65054MR2263496DOI10.1016/j.camwa.2006.08.017
  3. Bahuguna, D., Dabas, J., Shukla, R. K., Method of lines to hyperbolic integro-differential equations in ℝ n , Nonlinear Dyn. Syst. Theory 8 (2008), 317-328. (2008) Zbl1206.45010MR2482448
  4. Bátkai, A., Csomós, P., Nickel, G., 10.1007/s00028-009-0026-6, J. Evol. Equ. 9 (2009), 613-636. (2009) Zbl1239.47031MR2529739DOI10.1007/s00028-009-0026-6
  5. Berger, M. A., Mizel, V. J., Volterra equations with Ito integrals I, J. Integral Equations 2 (1980), 187-245. (1980) Zbl0442.60064MR0581430
  6. Prato, G. Da, Zabczyk, J., 10.1017/CBO9780511666223, Encyclopedia of Mathematics and Its Applications 44, Cambridge University Press, Cambridge (1992). (1992) Zbl0761.60052MR1207136DOI10.1017/CBO9780511666223
  7. Debbi, L., Dozzi, M., On a space discretization scheme for the fractional stochastic heat equations, Avaible at https://arxiv.org/abs/1102.4689v1. 
  8. Friedman, A., Stochastic Differential Equations and Applications, Vol. 1, Probability and Mathematical Statistics 28, Academic Press, New York (1975). (1975) Zbl0323.60056MR0494490
  9. Funaki, T., 10.2969/jmsj/03140719, J. Math. Soc. Japan 31 (1979), 719-744. (1979) Zbl0405.60067MR0544688DOI10.2969/jmsj/03140719
  10. Holden, H., Øksendal, B., Ubøe, J., Zhang, T., 10.1007/978-1-4684-9215-6, Probability and Its Applications, Birkhäuser, Basel (1996). (1996) Zbl0860.60045MR1408433DOI10.1007/978-1-4684-9215-6
  11. Kamont, Z., 10.1007/978-94-011-4635-7, Mathematics and Its Applications 486, Kluwer Academic Publishers, Dordrecht (1999). (1999) Zbl0973.35188MR1784260DOI10.1007/978-94-011-4635-7
  12. Kim, J. U., 10.1016/j.jfa.2010.08.017, J. Funct. Anal. 259 (2010), 3328-3359. (2010) Zbl1203.35293MR2727647DOI10.1016/j.jfa.2010.08.017
  13. Klebaner, F. C., 10.1142/p386, Imperial College Press, London (2005). (2005) Zbl1077.60001MR2160228DOI10.1142/p386
  14. Kreiss, H.-O., Scherer, G., 10.1137/0729041, SIAM J. Numer. Anal. 29 (1992), 640-646. (1992) Zbl0754.65078MR1163349DOI10.1137/0729041
  15. Leszczyński, H., 10.1515/GMJ.2000.97, Georgian Math. J. 7 (2000), 97-116. (2000) Zbl0964.35075MR1768048DOI10.1515/GMJ.2000.97
  16. Leszczyński, H., 10.1515/jaa.2011.009, J. Appl. Anal. 17 (2011), 137-154. (2011) Zbl1276.34065MR2805852DOI10.1515/jaa.2011.009
  17. McDonald, S., Finite difference approximation for linear stochastic partial differential equation with method of lines, MPRA Paper No. 3983. Avaible at http://mpra.ub.uni-muenchen.de/3983 (2006). (2006) 
  18. Quer-Sardanyons, L., Sanz-Solé, M., 10.1007/s11118-005-9002-0, Potential Anal. 24 (2006), 303-332. (2006) Zbl1119.60061MR2224753DOI10.1007/s11118-005-9002-0
  19. Reddy, S. C., Trefethen, L. N., 10.1007/BF01396228, Numer. Math. 62 (1992), 235-267. (1992) Zbl0734.65077MR1165912DOI10.1007/BF01396228
  20. Rößler, A., Seaïd, M., Zahri, M., 10.1016/j.amc.2007.09.062, Appl. Math. Comput. 199 (2008), 301-314. (2008) Zbl1142.65007MR2415825DOI10.1016/j.amc.2007.09.062
  21. Sharma, K. K., Singh, P., 10.1016/j.amc.2007.12.051, Appl. Math. Comput. 201 (2008), 229-238. (2008) Zbl1155.65374MR2432598DOI10.1016/j.amc.2007.12.051
  22. Yoo, H., 10.1090/S0025-5718-99-01150-3, Math. Comput. 69 (2000), 653-666. (2000) Zbl0942.65006MR1654030DOI10.1090/S0025-5718-99-01150-3

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.