References
- S.M. Allen and J.W. Cahn, A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening, Acta Metallurgica 27 (1979), pp. 1085–1095.
- D.C. Antonopoulou, Space–time discontinuous Galerkin methods for the ε-dependent stochastic Allen–Cahn equation with mild noise, IMA J. Numer. Anal. 40 (2020), pp. 2076–2105.
- D.C. Antonopoulou, G. Karali, and A. Millet, Existence and regularity of solution for a stochastic Cahn–Hilliard/Allen–Cahn equation with unbounded noise diffusion, J. Differ. Equ. 260 (2016), pp. 2383–2417.
- S. Azam, J.E. Macías-Díaz, N. Ahmed, I. Khan, M.S. Iqbal, M. Rafiq, K.S. Nisar, and M.O. Ahmad, Numerical modeling and theoretical analysis of a nonlinear advection-reaction epidemic system, Comput. Methods. Programs. Biomed. 193 (2020), p. 105429.
- M. Beneš, V. Chalupeckỳ, and K. Mikula, Geometrical image segmentation by the Allen–Cahn equation, Appl. Numer. Math. 51 (2004), pp. 187–205.
- F. Bertacco, Stochastic Allen–Cahn equation with logarithmic potential, Nonlinear Anal. 202 (2021), p. 112122.
- F.F. Bonsall and K. Vedak, Lectures on Some Fixed Point Theorems of Functional Analysis, Vol. 26, Bombay, Tata Institute of Fundamental Research Bombay, 1962.
- C.E. Bréhier and L. Goudenège, Analysis of some splitting schemes for the stochastic Allen-Cahn equation, Discrete Continuous Dyn. Syst.-Ser. B 24 (2019), pp. 4169–4190.
- C.E. Bréhier and L. Goudenège, Weak convergence rates of splitting schemes for the stochastic Allen–Cahn equation, BIT Numerical Math. 60 (2020), pp. 543–582.
- C. Chen, T. Dang, and J. Hong, An adaptive time-stepping full discretization for stochastic Allen–Cahn equation, (2021). Preprint arXiv:2108.01909.
- L.Q. Chen, Phase-field models for microstructure evolution, Annu. Rev. Mater. Res. 32 (2002), pp. 113–140.
- M.P. D'Arienzo and L. Rarità, Growth effects on the network dynamics with applications to the cardiovascular system, in AIP Conference Proceedings, Vol. 2293, New York, AIP Publishing, 2020.
- M.P. D'Arienzo and L. Rarità, Management of supply chains for the wine production, in AIP Conference Proceedings, Vol. 2293, AIP Publishing, 2020.
- L.C. Evans, An Introduction to Stochastic Differential Equations, Vol. 82, American Mathematical Society, Rhode Island, 2012.
- X. Feng, Y. Li, and Y. Zhang, Finite element methods for the stochastic Allen–Cahn equation with gradient-type multiplicative noise, SIAM. J. Numer. Anal. 55 (2017), pp. 194–216.
- M. Kamrani and S.M. Hosseini, The role of coefficients of a general SPDE on the stability and convergence of a finite difference method, J. Comput. Appl. Math. 234 (2010), pp. 1426–1434.
- G.D. Karali and Y. Nagase, On the existence of solution for a Cahn-Hilliard/Allen-Cahn equation, Discrete Continuous Dyn. Syst.-Ser. S (DCDS-S) 7 (2014), pp. 127–137.
- M. Kovács, S. Larsson, and F. Lindgren, On the backward Euler approximation of the stochastic Allen-Cahn equation, J. Appl. Probab. 52 (2015), pp. 323–338.
- M. Kovács and E. Sikolya, On the stochastic Allen-Cahn equation on networks with multiplicative noise, Electron. J. Qual. Theory. Differ. Equ. (2021), (5192–3), pp. 187–205.
- A.K. Majee and A. Prohl, Optimal strong rates of convergence for a space-time discretization of the stochastic Allen–Cahn equation with multiplicative noise, Comput. Methods Appl. Math. 18 (2018), pp. 297–311.
- T.T. Medjo, On the existence and uniqueness of solution to a stochastic 2D Cahn–Hilliard–Navier–Stokes model, J. Differ. Equ. 263 (2017), pp. 1028–1054.
- C. Mircioiu, V. Voicu, V. Anuta, A. Tudose, C. Celia, D. Paolino, M. Fresta, R. Sandulovici, and I. Mircioiu, Mathematical modeling of release kinetics from supramolecular drug delivery systems, Pharmaceutics 11 (2019), p. 140.
- L. Rarità, A genetic algorithm to optimize dynamics of supply chains, in Optimization in Artificial Intelligence and Data Sciences: ODS, First Hybrid Conference, September 14–17, Springer, Rome, Italy, 2022, pp. 107–115.
- L. Rarità, I. Stamova, and S. Tomasiello, Numerical schemes and genetic algorithms for the optimal control of a continuous model of supply chains, Appl. Math. Comput. 388 (2021), p. 125464.
- A. Raza, N. Ahmed, and M. Rafiq, Analysis of a nonstandard computer method to simulate a nonlinear stochastic epidemiological model of coronavirus-like diseases, Comput. Methods. Programs. Biomed. 204 (2021), p. 106054.
- M.D. Ryser, N. Nigam, and P.F. Tupper, On the well-posedness of the stochastic Allen–Cahn equation in two dimensions, J. Comput. Phys. 231 (2012), pp. 2537–2550.
- S.S. Sana, A structural mathematical model on two echelon supply chain system, Ann. Oper. Res. 315 (2022), pp. 1997–2025.
- J. Schauder, Der fixpunktsatz in funktionalraümen, Studia Math. 2 (1930), pp. 171–180.
- A. Shah, M. Sabir, and P. Bastian, An efficient time-stepping scheme for numerical simulation of dendritic crystal growth, Eur. J. Comput. Mech. 25 (2016), pp. 475–488.
- A. Shah, M. Sabir, M. Qasim, and P. Bastian, Efficient numerical scheme for solving the Allen-Cahn equation, Numer. Methods. Partial. Differ. Equ. 34 (2018), pp. 1820–1833.
- T. Shardlow, Stochastic perturbations of the Allen–Cahn equation, Electronic J. Differ. Equations 2000 (2000), pp. 1–19.
- S. Singh, Phase transitions in liquid crystals, Phys. Rep. 324 (2000), pp. 107–269.
- J.M. Villarreal, Approximate Solutions to the Allen-Cahn Equation Using the Finite Difference Method, Ph.D. diss., Texas A&M International University, 2016.
- X. Wang, An efficient explicit full-discrete scheme for strong approximation of stochastic Allen–Cahn equation, Stoch. Process. Their. Appl. 130 (2020), pp. 6271–6299.
- O.J. Watson, G. Barnsley, J. Toor, A.B. Hogan, P. Winskill, and A.C. Ghani, Global impact of the first year of COVID-19 vaccination: a mathematical modelling study, The Lancet Infectious Diseases 22 (2022), pp. 1293–1302.
- M.W. Yasin, M.S. Iqbal, N. Ahmed, A. Akgül, A. Raza, M. Rafiq, and M.B. Riaz, Numerical scheme and stability analysis of stochastic Fitzhugh–Nagumo model, Res. Phys. 32 (2022), p. 105023.
- M.W. Yasin, M.S. Iqbal, A.R. Seadawy, M.Z. Baber, M. Younis, and S.T. Rizvi, Numerical scheme and analytical solutions to the stochastic nonlinear advection diffusion dynamical model, Int. J. Nonlinear Sci. Numer. Simul. 24 (2021), pp. 467–487.