A second-order box solver for nonlinear delayed convection-diffusion equations with Neumann boundary conditions

References

• R. Abazaria and M. Ganjib, Extended two-dimensional DTM and its application on nonlinear PDEs with proportional delay, Int. J. Comput. Math. 88 (2011), pp. 1749–1762. doi: 10.1080/00207160.2010.526704
   Web of Science ®Google Scholar
• A.R. Ansari, S.A. Bakr, and G.I. Shishkin, A parameter-robust finite difference method for singularly perturbed delay parabolic partial differential equations, J. Comput. Appl. Math. 205 (2007), pp. 552–566. doi: 10.1016/j.cam.2006.05.032
   Web of Science ®Google Scholar
• H.Y. Cao and Z.Z. Sun, A second-order linearized difference scheme for a strongly coupled reaction-diffusion system, Numer. Methods Partial Differ. Equ. 24 (2008), pp. 9–23. doi: 10.1002/num.20232
   Web of Science ®Google Scholar
• M.A. Castro, F. Rodríguez, J. Cabrera, and J.A. Martín, Difference schemes for time-dependent heat conduction models with delay, Int. J. Comput. Math. 91 (2014), pp. 53–61. doi: 10.1080/00207160.2013.779371
   Web of Science ®Google Scholar
• D. Deng, The study of a fourth-order multistep ADI method applied to nonlinear delay reaction-diffusion equations, Appl. Numer. Math. 96 (2015), pp. 118–133. doi: 10.1016/j.apnum.2015.05.007
   Web of Science ®Google Scholar
• P. García, M.A. Castro, J.A. Martín, and A. Sirvent, Numerical solutions of diffusion mathematical models with delay, Math. Comput. Model. 50 (2009), pp. 860–868. doi: 10.1016/j.mcm.2009.05.015
   Google Scholar
• Q. He, L. Kang, and D.J. Evans, Convergence and stability of the finite difference scheme for nonlinear parabolic systems with time delay, Numer. Algor. 16 (1997), pp. 129–153. doi: 10.1023/A:1019130928606
   Web of Science ®Google Scholar
• Z. Jackiewicz and B. Zubik-Kowal, Spectral collocation and waveform relaxation methods for nonlinear delay partial differential equations, Appl. Numer. Math. 56 (2006), pp. 433–443. doi: 10.1016/j.apnum.2005.04.021
   Web of Science ®Google Scholar
• D. Li, C. Zhang, and H. Qin, LDG method for reaction-diffusion dynamical systems with time delay, Appl. Math. Comput. 217 (2011), pp. 9173–9181.
   Web of Science ®Google Scholar
• D. Li, C. Zhang, and J. Wen, A note on compact finite difference method for reaction-diffusion equations with delay, Appl. Math. Model. 39 (2015), pp. 1749–1754. doi: 10.1016/j.apm.2014.09.028
   Web of Science ®Google Scholar
• H. Liang, Convergence and asymptotic stability of Galerkin methods for linear parabolic equations with delays, Appl. Math. Comput. 264 (2015), pp. 160–178.
   Web of Science ®Google Scholar
• H. Liang, D. Shi, and W. Lv, Convergence and asymptotic stability of Galerkin methods for a partial differential equation with piecewise constant argument, Appl. Math. Comput. 217 (2010), pp. 854–860.
   Web of Science ®Google Scholar
• H. Liang, M.Z. Liu, and W. Lv, Stability of θ- schemes in the numerical solution of a partial differential equation with piecewise continuous arguments, Appl. Math. Lett. 23 (2010), pp. 198–206. doi: 10.1016/j.aml.2009.09.012
   Web of Science ®Google Scholar
• J.M. Liu and Z.Z. Sun, Finite difference method for reaction-diffusion with nonlocal boundary conditions, Numer. Math. J. Chinese Univ. (English Ser.) 2 (2007), pp. 97–111.
   Google Scholar
• Z.Z. Sun, A class of second-order accurate difference schemes for quasi-linear parabolic differential equations, Math. Numer. Sinica (in Chinese) 16 (1994), pp. 347–361.
   Google Scholar
• Z.Z. Sun, The Method of Order Reduction and its Application to the Numerical Solutions of Partial Differential Equations, Science Press, Beijing, China, 2009.
   Google Scholar
• Z.Z. Sun and Z.B. Zhang, A linearized compact difference scheme for a class of nonlinear delay partial differential equations, Appl. Math. Model. 37 (2013), pp. 742–752. doi: 10.1016/j.apm.2012.02.036
   Web of Science ®Google Scholar
• H. Tian, Asymptotic stability analysis of the linear θ-method for linear parabolic differential equations with delay, J. Differ. Equ. Appl. 15 (2009), pp. 473–487. doi: 10.1080/10236190802128284
   Web of Science ®Google Scholar
• P.J. Van Der Houwen, B.P. Sommeijer, and C.T.H. Baker, On the stability of predictor-corrector methods for parabolic equations with delay, IMA J. Numer. Anal. 6 (1986), pp. 1–23. doi: 10.1093/imanum/6.1.1
   Web of Science ®Google Scholar
• Y. Wang, An efficient computational method for a class of singularly perturbed delay parabolic partial differential equation, Int. J. Comput. Math. 88 (2011), pp. 3496–3506. doi: 10.1080/00207160.2011.600450
   Web of Science ®Google Scholar
• J. Wu, Theory and Applications of Partial Functional Differential Equations, Springer-Verlag, New York, 1996.
   Google Scholar
• Y.L. Zhang and Z.Z. Sun, A second-order linearized finite difference scheme for the generalized Fiser-Kolmogorov-Petrovskii-Piskunov equation, Int. J. Comput. Math. 88 (2011), pp. 3394–3405. doi: 10.1080/00207160.2011.581362
   Web of Science ®Google Scholar
• Q. Zhang and C. Zhang, A compact difference scheme combined with extrapolation techniques for solving a class of neutral delay parabolic differential equations, Appl. Math. Lett. 26 (2013), pp. 306–312. doi: 10.1016/j.aml.2012.09.015
   Web of Science ®Google Scholar
• Q. Zhang, C. Zhang, and L. Wang, The compact and Crank-Nicolson ADI schemes for two-dimensional semilinear multidelay parabolic equations, J. Comput. Appl. Math. 306 (2016), pp. 217–230. doi: 10.1016/j.cam.2016.04.016
   Web of Science ®Google Scholar