Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems
Béla J. Szekeres; Ferenc Izsák
Applications of Mathematics (2017)
- Volume: 62, Issue: 1, page 15-36
- ISSN: 0862-7940
Access Full Article
topAbstract
topHow to cite
topReferences
top- Abatangelo, N., Dupaigne, L., 10.1016/j.anihpc.2016.02.001, To appear in Ann. Inst. Henri Poincaré, Anal. Non. Linéaire (2016). (2016) MR3610940DOI10.1016/j.anihpc.2016.02.001
- Bátkai, A., Csomós, P., Farkas, B., Semigroups for Numerical Analysis, Internet-Seminar Manuscript, 2012, tt{https://isem-mathematik.uibk.ac.at}.
- Benson, D. A., Wheatcraft, S. W., Meerschaert, M. M., 10.1029/2000wr900031, Water Resour. Res. 36 (2000), 1403-1412. (2000) DOI10.1029/2000wr900031
- Canuto, C., Quarteroni, A., 10.1007/bf02576357, Calcolo 18 (1981), 197-217. (1981) Zbl0485.65078MR0647825DOI10.1007/bf02576357
- Nezza, E. Di, Palatucci, G., Valdinoci, E., 10.1016/j.bulsci.2011.12.004, Bull. Sci. Math. 136 (2012), 521-573. (2012) Zbl1252.46023MR2944369DOI10.1016/j.bulsci.2011.12.004
- Du, Q., Gunzburger, M., Lehoucq, R. B., Zhou, K., 10.1137/110833294, SIAM Rev. 54 (2012), 667-696. (2012) Zbl06122544MR3023366DOI10.1137/110833294
- Du, Q., Gunzburger, M., Lehoucq, R. B., Zhou, K., 10.1142/S0218202512500546, Math. Models Methods Appl. Sci. 23 (2013), 493-540. (2013) Zbl1266.26020MR3010838DOI10.1142/S0218202512500546
- A. M. Edwards, R. A. Phillips, N. W. Watkins, M. P. Freeman, E. J. Murphy, V. Afanasyev, S. V. Buldyrev, M. G. E. da Luz, E. P. Raposo, H. E. Stanley, G. M. Viswanathan, 10.1038/nature06199, Nature 449 (2007), 1044-1048. (2007) MR2550512DOI10.1038/nature06199
- Engel, K.-J., Nagel, R., 10.1007/b97696, Graduate Texts in Mathematics 194, Springer, Berlin (2000). (2000) Zbl0952.47036MR1721989DOI10.1007/b97696
- Feng, L. B., Zhuang, P., Liu, F., Turner, I., 10.1016/j.amc.2014.12.060, Appl. Math. Comput. 257 (2015), 52-65. (2015) Zbl1339.65144MR3320648DOI10.1016/j.amc.2014.12.060
- Gradshteyn, I. S., Ryzhik, I. M., 10.1016/b978-0-12-294757-5.x5000-4, Academic Press, San Diego (2000). (2000) Zbl0981.65001MR1773820DOI10.1016/b978-0-12-294757-5.x5000-4
- Ilic, M., Liu, F., Turner, I., Anh, V., Numerical approximation of a fractional-in-space diffusion equation. I, Fract. Calc. Appl. Anal. 8 (2005), 323-341. (2005) Zbl1126.26009MR2252038
- Ilic, M., Liu, F., Turner, I., Anh, V., Numerical approximation of a fractional-in-space diffusion equation. II. With nonhomogeneous boundary conditions, Fract. Calc. Appl. Anal. 9 (2006), 333-349. (2006) Zbl1132.35507MR2300467
- Ilić, M., Turner, I. W., Simpson, D. P., 10.1093/imanum/drp003, IMA J. Numer. Anal. 30 (2010), 1044-1061. (2010) Zbl1220.65052MR2727815DOI10.1093/imanum/drp003
- Kilbas, A. A., Srivastava, H. M., Trujillo, J. J., 10.1016/s0304-0208(06)x8001-5, North-Holland Mathematics Studies 204, Elsevier, Amsterdam (2006). (2006) Zbl1092.45003MR2218073DOI10.1016/s0304-0208(06)x8001-5
- Li, C., Zhao, Z., Chen, Y., 10.1016/j.camwa.2011.02.045, Comput. Math. Appl. 62 (2011), 855-875. (2011) Zbl1228.65190MR2824676DOI10.1016/j.camwa.2011.02.045
- Liu, F., Zhuang, P., Anh, V., Turner, I., 10.21914/anziamj.v47i0.1030, ANZIAM J. 47 (2005), C48--C68. (2005) MR2226522DOI10.21914/anziamj.v47i0.1030
- Mainardi, F., Luchko, Y., Pagnini, G., The fundamental solution of the space-time fractional diffusion equation, Fract. Calc. Appl. Anal. 4 (2001), 153-192. (2001) Zbl1054.35156MR1829592
- Meerschaert, M. M., Tadjeran, C., 10.1016/j.cam.2004.01.033, J. Comput. Appl. Math. 172 (2004), 65-77. (2004) Zbl1126.76346MR2091131DOI10.1016/j.cam.2004.01.033
- Michelitsch, T., Maugin, G., Nowakowski, A., Nicolleau, F., Rahman, M., 10.2478/s13540-013-0052-5, Fract. Calc. Appl. Anal. 16 (2013), 827-859. (2013) Zbl1314.35209MR3124339DOI10.2478/s13540-013-0052-5
- Nochetto, R. H., Otárola, E., Salgado, A. J., 10.1007/s10208-014-9208-x, Found. Comput. Math. 15 (2015), 733-791. (2015) Zbl1347.65178MR3348172DOI10.1007/s10208-014-9208-x
- Pasciak, J. E., 10.2307/2006376, Math. Comput. 35 (1980), 1081-1092. (1980) Zbl0448.65071MR583488DOI10.2307/2006376
- Podlubny, I., 10.1016/s0076-5392(99)x8001-5, Mathematics in Science and Engineering 198, Academic Press, San Diego (1999). (1999) Zbl0924.34008MR1658022DOI10.1016/s0076-5392(99)x8001-5
- Samko, S. G., Kilbas, A. A., Marichev, O. I., Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, New York (1993). (1993) Zbl0818.26003MR1347689
- Szekeres, B. J., Izsák, F., 10.1515/math-2015-0056, Open Math. (electronic only) 13 (2015), 581-600. (2015) Zbl06632236MR3403508DOI10.1515/math-2015-0056
- Szekeres, B. J., Izsák, F., 10.1016/j.cam.2015.07.026, J. Comput. Appl. Math. 292 (2016), 553-561. (2016) Zbl1327.65215MR3392412DOI10.1016/j.cam.2015.07.026
- Tadjeran, C., Meerschaert, M. M., Scheffler, H.-P., 10.1016/j.jcp.2005.08.008, J. Comput. Phys. 213 (2006), 205-213. (2006) Zbl1089.65089MR2203439DOI10.1016/j.jcp.2005.08.008
- Tian, W., Zhou, H., Deng, W., 10.1090/S0025-5718-2015-02917-2, Math. Comput. 84 (2015), 1703-1727. (2015) Zbl1318.65058MR3335888DOI10.1090/S0025-5718-2015-02917-2
- Yang, Q., Turner, I., Moroney, T., Liu, F., 10.1016/j.apm.2014.02.005, Appl. Math. Model. 38 (2014), 3755-3762. (2014) MR3233804DOI10.1016/j.apm.2014.02.005
- Zhou, H., Tian, W., Deng, W., 10.1007/s10915-012-9661-0, J. Sci. Comput. 56 (2013), 45-66. (2013) Zbl1278.65130MR3049942DOI10.1007/s10915-012-9661-0