Previous Articles Next Articles
Haiyan Yuan
Haiyan Yuan. CONVERGENCE AND MEAN-SQUARE STABILITY OF EXPONENTIAL EULER METHOD FOR SEMI-LINEAR STOCHASTIC DELAY INTEGRO-DIFFERENTIAL EQUATIONS[J]. Journal of Computational Mathematics, 2022, 40(2): 177-204.
[1] A. Al-Mutib, Stability properties of numerical methods for solving delay differential equations, J. Comput. Appl. Math., 10(1984), 71-79. [2] V. Barwell, Special stability problems for functional differential equations, BIT, 15(1975), 130- 135. [3] C. Baker, E. Buckwar, Exponential stability in p-th mean of solutions, and of convergent Eulertype solutions, of stochastic delay differential equations, J. Comput. Appl. Math., 184(2005), 404-427. [4] K. Dekker, J. Verwer, Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations, CWI Monographs, 2, North-Holland, Amsterdam, 1984. [5] X. Ding, K. Wu, M. Liu, Convergence and stability of the semi-implicit Euler method for linear stochastic delay integro-differential equations, Int. J. Comput. Math., 83(2006), 753-763. [6] W.H. Enright, Continuous numerical methods for ODEs with defect control, J. Comput. Appl. Math., 125(2000), 159-170. [7] D. Higham, X. Mao, A. Stuart, Exponential mean-square stability of numerical solutions to stochastic differential equations, LMS J. Comput. Math., 6(2003), 297-313. [8] M. Hochbruck, A. Ostermann, Explicit exponential Runge-Kutta methods for semilinear parabolic problems, SIAM J. Numer. Anal., 43(2005), 1069-1090. [9] M. Hochbruck, A. Ostermann, J. Schweitzer, Exponential Rosenbrock-type methods, SIAM J. Numer. Anal., 47(2009), 786-803. [10] M. Hochbruck, A. Ostermann, Exponential integrators, Acta Numer., 19(2010), 209-286. [11] F. Jiang, Y. Shen, J. Hu, Stability of the split-step backward Euler scheme for stochastic delay integro-differential equations with Markovian switching, Commun. Nonlinear Sci., 16(2011), 814- 821. [12] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, San Diego, 1993. [13] V. Kolmanovskii, A. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations, Kluwer Academic Publishers, Dordrecht, 1999. [14] M. Kassem, M. Hussein, A second-order accurate numerical method for a semilinear integrodifferential equation with a weakly singular kernel, IMA J. Numer. Anal., 30(2010), 555-578. [15] P.E. Kloeden, G.J. Lord, A. Neuenkirch, T. Shardlow, The exponential integrator scheme for stochastic partial differential equations:pathwise error bounds, J. Comput. Appl. Math., 235(2011), 1245-1260. [16] I. Kyza, C. Makridakis, Analysis for time discrete approximations of blow-up solutions of semilinear parabolic equations, SIAM J. Numer. Anal., 49(2011), 405-426. [17] J.D. Lawson, Generalized Runge-Kutta processes for stable systems with large Lipschitz constants, SIAM J. Numer. Anal., 4(1967), 372-380. [18] Q. Li, S. Gan, Mean-square exponential stability of stochastic theta methods for nonlinear stochastic delay integro-differential equations, J. Appl. Math. Comput., 39(2012), 69-87. [19] V.T. Luan, A. Ostermann, Exponential B-series:The stff case, SIAM J. Numer. Anal., 51(2013), 3431-3445. [20] V.T. Luan, A. Ostermann, Exponential Rosenbrock methods of order five construction, analysis and numerical comparisons, J. Comput. Appl. Math., 255(2014), 417-431. [21] V.T. Luan, A. Ostermann, Explicit exponential Runge-Kutta methods of high order for parabolic problems, J. Comput. Appl. Math., 256(2014), 168-179. [22] X. Mao, The LaSalle-type theorems for stochastic differential equations, Adv. Nonlinear Stud., 7(2000), 307-328. [23] X. Mao, A note on the LaSalle-type theorems for stochastic differential delay equations, J. Math. Anal. Appl., 268(2002), 125-142. [24] B. Minchev, W. Wright, A review of exponential integrators for first order semi-linear problems, preprint, 2005. [25] C.M. Mora, Weak exponential schemes for stochastic differential equations with additive noise, IMA J. Numer. Anal., 25(2005), 486-506. [26] X. Mao, Stochastic Differential Equations and Applications, Horwood Publishing Limited, Chichester, second edition, 2008. [27] S. Maset, M. Zennaro, Unconditional stability of explicit exponential Runge-Kutta methods for semi-linear ordinary differential equations, Math. Comput., 78(2009), 957-967. [28] S. Maset, M. Zennaro, Stability properties of explicit exponential Runge-Kutta methods, IMA J. Numer. Anal., 33(2013), 111-135. [29] F. Mirzaee, E. Hadadiyan, A collocation technique for solving nonlinear stochastic Itô-Volterra integral equations, Appl. Math. Comput., 247(2014), 1011-1020. [30] F. Mirzaee, N. Samadyar, Numerical solution of nonlinear stochastic Itô-Volterra integral equations driven by fractional Brownian motion, Math. Method Appl. Sci., 41(2018), 1410-1423. [31] A. Ostermann, M. Thalhammer, W. Wright, A class of explicit exponential general linear methods, BIT, 46(2006), 409-431. [32] U.A. Osisiogu, F.E. Bazuaye, Construction of extended exponential general linear methods, INT J. Appl. Math., 27(2014), 263-281. [33] A. Rathinasamy, K. Balachandran, Mean-square stability of Milstein method for linear hybrid stochastic delay integro-differential equations, Nonlinear Anal. Hybri., 2(2008), 1256-1263. [34] Y. Ren, Y. Qin, R. Sakthivel, Existence results for fractional order semilinear integro-differential evolution equations with infinite delay, Integr. Equ. Oper. Th., 67(2010), 33-49. [35] L. E. Shaikhet, J.A. Roberts, Reliability of difference analogues to preserve stability properties of stochastic volterra integro-differential equations, Adv. Differ. Equ.-Ny, 2016(2006), 1-23. [36] Q. Wu, L. Hu, Z. Zhang, Convergence and stability of balanced methods for stochastic delay integro-differential equations, Appl. Math. Comput., 237(2014), 446-460. [37] L. Xu, Some notes on linear growth condition, J. Hubei Normal University (Natural Science), 28(2008), 13-16. [38] M. Zennaro, Natural continuous extensions of Runge-Kutta methods, Math. Comput., 46(1986), 119-133. [39] L. Zhang, Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations, J. Inequal. Appl., 249(2017), 249-268. [40] J. Zhao, R. Zhan, Y. Xu, D-convergence and conditional GDN-stability of exponential RungeKutta methods for semilinear delay differential equations, Appl. Math. Comput., 339(2018), 45-58. |
[1] | Minfu Feng, Yanhong Bai, Yinnian He, Yanmei Qin. A NEW STABILIZED SUBGRID EDDY VISCOSITY METHOD BASED ON PRESSURE PROJECTION AND EXTRAPOLATED TRAPEZOIDAL RULE FOR THE TRANSIENT NAVIER-STOKES EQUATIONS [J]. Journal of Computational Mathematics, 2011, 29(4): 415-440. |
Viewed | ||||||
Full text |
|
|||||
Abstract |
|
|||||