On solving some stochastic delay differential equations by Daubechies wavelet

References

• Beuter A, Bélair J, Labrie C. Feedback and delays in neurological diseases: a modelling study using dynamical systems. Bull Math Biol. 1993;55(3):525–541.
   PubMed Web of Science ®Google Scholar
• Eurich CW, Milton JG. Noise-induced transitions in human postural sway. Phys Rev E. 1996;54(6):6681–6684. doi:10.1103/PhysRevE.54.6681
   PubMed Web of Science ®Google Scholar
• Mackey MC, Longtin A, Milton JG, et al. Noise and critical behaviour of the pupil light reflex at oscillation onset. Phys Rev A. 1990;41(12):6992–7005. doi:10.1103/PhysRevA.41.6992
   PubMed Web of Science ®Google Scholar
• Gábor S. Delay-differential equation models for machine tool chatter. Nonlinear Dyn Mater Process Manuf. 1998:165–192.
   Google Scholar
• Tsypkin Y. The systems with delayed feedback. Avtomat Telemekh. 1928;7:107–129.
   Google Scholar
• Gábor O, Wilson RE, Gábor S. Traffic jams: dynamics and control. Philos Trans Royal Soc London A: Math Phys Eng Sci. 2010;368(1928):4455–4479.
   PubMed Web of Science ®Google Scholar
• Volterra V. Sur la théorie mathématique des phénoménes héréditaires. J Math Pures Appl. 1928;7:149–192.
   Google Scholar
• Ann CS. Time delays in neural systems. Berlin, Heidelberg: Springer Berlin Heidelberg; 2007; p. 65–90.
   Google Scholar
• Mirzaee F, Samadyar N. Combination of finite difference method and meshless method based on radial basis functions to solve fractional stochastic advection–diffusion equations. Eng Comput. 2020;36(4):1673–1686. doi:10.1007/s00366-019-00789-y
   Web of Science ®Google Scholar
• Samadyar N, Ordokhani Y, Mirzaee F. Hybrid Taylor and block-pulse functions operational matrix algorithm and its application to obtain the approximate solution of stochastic evolution equation driven by fractional Brownian motion. Commun Nonlinear Sci Numer Simul. 2020;90:Article ID 105346. doi:10.1016/j.cnsns.2020.105346
   Web of Science ®Google Scholar
• Samadyar N, Ordokhani Y, Mirzaee F. The couple of hermite-based approach and Crank–Nicolson scheme to approximate the solution of two dimensional stochastic diffusion-wave equation of fractional order. Eng Anal Bound Elem. 2020;118:285–294. doi:10.1016/j.enganabound.2020.05.010
   Web of Science ®Google Scholar
• Yin Z, Gan S. Chebyshev spectral collocation method for stochastic delay differential equations. Adv Differ Equ. 2015;2015(1):113. doi:10.1186/s13662-015-0447-1
   Google Scholar
• Zhu Q. Stability analysis of stochastic delay differential equations with Lévy noise. Syst Control Lett. 2018;118:62–68. doi:10.1016/j.sysconle.2018.05.015
   Web of Science ®Google Scholar
• Kloeden P, Platen E. Numerical solution of stochastic differential equations. Springer; 1995.
   Google Scholar
• Shariati NM, Yaghouti M, Alipanah A. A convergent wavelet-based method for solving linear stochastic differential equations included 1D and 2D noise. J Stat Comput Simul. 2023;93(5):837–861. doi:10.1080/00949655.2022.2122969
   Web of Science ®Google Scholar
• Mikosch T. Elementary stochastic calculus. World Scientific; 2000.
   Google Scholar
• Beretta E, Carletti M, Solimano F. On the effects of environmental fluctuations in a simple model of bacteria-bacteriophage interaction. Can Appl Math Q. 2000;8(4):321–366. doi:10.1216/camq/1032375139
   Google Scholar
• Cordoni F, Di Persio L, Oliva I. Stochastic delay differential equations with jumps and applications in mathematical finance; 2014. preprint.
   Google Scholar
• Baker CTH, Buckwar E. Numerical analysis of explicit one-step methods for stochastic delay differential equations. LMS J Comput Math. 2000;3:315–335. doi:10.1112/S1461157000000322
   Google Scholar
• Wang ZQ, Wang LL. A Legendre–Gauss collocation method for nonlinear delay differential equations. Discrete Continuous Dyn Syst Ser B. 2010;13(3):685–708. doi:10.3934/dcdsb.2010.13.685
   Web of Science ®Google Scholar
• Soheili AR, Soleymani F. A new solution method for stochastic differential equations via collocation approach. Int J Comput Math. 2016;93(12):2079–2091. doi:10.1080/00207160.2015.1085029
   Web of Science ®Google Scholar
• Huanga C, Ganb S, Wangc D. Delay-dependent stability analysis of numerical methods for stochastic delay differential equations. J Comput Appl Math. 2012;236(14):3514–3527. doi:10.1016/j.cam.2012.03.003
   Web of Science ®Google Scholar
• Pan GW. Wavelets in electromagnetics and device modeling. Wiley-Interscience; 2003.
   Google Scholar
• Walnut D. An introduction to wavelet analysis. Basel, Switzerland: Birkhäuser; 2002.
   Google Scholar
• Daubechies I. Orthonormal basis of compactly supported wavelets. Commun Pure Appl Math. 1988;41(7):909–996. doi:10.1002/cpa.v41:7
   Web of Science ®Google Scholar
• Daubechies I. Ten lectures on wavelets. 1992. (Society for industrial and applied mathematics).
   Google Scholar
• Cohen A. Numerical analysis of wavelet methods. North Holland: Elsevier; 2003.
   Google Scholar
• Beylkin G. On the representation of operators in bases of compactly supported wavelets. J Numer Anal. 1992;29(6):1716–1740. doi:10.1137/0729097
   Web of Science ®Google Scholar