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Numerical Methods for Delay Differential Equations

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Cited by:

  1. Tan, Zengqiang & Zhang, Chengjian, 2022. "Numerical approximation to semi-linear stiff neutral equations via implicit–explicit general linear methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 68-87.
  2. Eriqat, Tareq & El-Ajou, Ahmad & Oqielat, Moa'ath N. & Al-Zhour, Zeyad & Momani, Shaher, 2020. "A New Attractive Analytic Approach for Solutions of Linear and Nonlinear Neutral Fractional Pantograph Equations," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
  3. Qin, Hongyu & Zhang, Qifeng & Wan, Shaohua, 2019. "The continuous Galerkin finite element methods for linear neutral delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 76-85.
  4. Qin, Tingting & Zhang, Chengjian, 2015. "Stable solutions of one-leg methods for a class of nonlinear functional-integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 47-57.
  5. Zhao, Jingjun & Zhan, Rui & Xu, Yang, 2018. "D-convergence and conditional GDN-stability of exponential Runge–Kutta methods for semilinear delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 45-58.
  6. Bürger, Raimund & Ruiz-Baier, Ricardo & Tian, Canrong, 2017. "Stability analysis and finite volume element discretization for delay-driven spatio-temporal patterns in a predator–prey model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 28-52.
  7. Zhang, Gui-Lai & Song, Ming-Hui, 2019. "Impulsive continuous Runge–Kutta methods for impulsive delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 160-173.
  8. Zhao, Jingjun & Zhan, Rui & Xu, Yang, 2020. "Explicit exponential Runge–Kutta methods for semilinear parabolic delay differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 366-381.
  9. Alanazi, Khalaf M. & Jackiewicz, Zdzislaw & Thieme, Horst R., 2019. "Numerical simulations of spread of rabies in a spatially distributed fox population," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 159(C), pages 161-182.
  10. Amin, Rohul & Shah, Kamal & Asif, Muhammad & Khan, Imran, 2021. "A computational algorithm for the numerical solution of fractional order delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 402(C).
  11. Wang, Qi, 2015. "Numerical oscillation of neutral logistic delay differential equation," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 49-59.
  12. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
  13. Xu, Y. & Zhao, J.J., 2008. "Stability of Runge–Kutta methods for neutral delay-integro-differential-algebraic system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 571-583.
  14. Amat, Sergio & José Legaz, M. & Pedregal, Pablo, 2015. "A variable step-size implementation of a variational method for stiff differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 49-57.
  15. Zhang, G.L. & Song, Minghui & Liu, M.Z., 2015. "Asymptotical stability of the exact solutions and the numerical solutions for a class of impulsive differential equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 12-21.
  16. Cheng, Xue & Chen, Zhong & Zhang, Qingpu, 2015. "An approximate solution for a neutral functional–differential equation with proportional delays," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 27-34.
  17. Ashwin Aravindakshan & Prasad Naik, 2011. "How does awareness evolve when advertising stops? The role of memory," Marketing Letters, Springer, vol. 22(3), pages 315-326, September.
  18. Zhang, Chengjian & Chen, Hao, 2010. "Asymptotic stability of block boundary value methods for delay differential-algebraic equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 100-108.
  19. García, M.A. & Castro, M.A. & Martín, J.A. & Rodríguez, F., 2018. "Exact and nonstandard numerical schemes for linear delay differential models," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 337-345.
  20. V. Subburayan & N. Ramanujam, 2013. "An Initial Value Technique for Singularly Perturbed Convection–Diffusion Problems with a Negative Shift," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 234-250, July.
  21. Xiaohua Ding & Huan Su, 2007. "Dynamics of a Discretization Physiological Control System," Discrete Dynamics in Nature and Society, Hindawi, vol. 2007, pages 1-16, February.
  22. M. Motawi Khashan & Rohul Amin & Muhammed I. Syam, 2019. "A New Algorithm for Fractional Riccati Type Differential Equations by Using Haar Wavelet," Mathematics, MDPI, vol. 7(6), pages 1-12, June.
  23. Liping Wen & Xiong Liu & Yuexin Yu, 2015. "Stability of Runge-Kutta Methods for Neutral Delay Differential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-8, November.
  24. Posch, Olaf & Trimborn, Timo, 2010. "Numerical solution of continuous-time DSGE models under Poisson uncertainty," Hannover Economic Papers (HEP) dp-450, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  25. Rayal, Ashish & Ram Verma, Sag, 2020. "Numerical analysis of pantograph differential equation of the stretched type associated with fractal-fractional derivatives via fractional order Legendre wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
  26. Nasser Hassan Sweilam & Seham Mahyoub Al-Mekhlafi & Taghreed Abdul Rahman Assiri, 2017. "Numerical Study for Time Delay Multistrain Tuberculosis Model of Fractional Order," Complexity, Hindawi, vol. 2017, pages 1-14, July.
  27. Tan, Zengqiang & Zhang, Chengjian, 2018. "Implicit-explicit one-leg methods for nonlinear stiff neutral equations," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 196-210.
  28. Yan, Xiaoqiang & Zhang, Chengjian, 2019. "Solving nonlinear functional–differential and functional equations with constant delay via block boundary value methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 21-32.
  29. Beaghton, Andrea & Beaghton, Pantelis John & Burt, Austin, 2016. "Gene drive through a landscape: Reaction–diffusion models of population suppression and elimination by a sex ratio distorter," Theoretical Population Biology, Elsevier, vol. 108(C), pages 51-69.
  30. María Ángeles Castro & Miguel Antonio García & José Antonio Martín & Francisco Rodríguez, 2019. "Exact and Nonstandard Finite Difference Schemes for Coupled Linear Delay Differential Systems," Mathematics, MDPI, vol. 7(11), pages 1-14, November.
  31. Ashwin Aravindakshan & Prasad A. Naik, 2015. "Understanding the Memory Effects in Pulsing Advertising," Operations Research, INFORMS, vol. 63(1), pages 35-47, February.
  32. Kürkçü, Ömür Kıvanç & Aslan, Ersin & Sezer, Mehmet, 2016. "A numerical approach with error estimation to solve general integro-differential–difference equations using Dickson polynomials," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 324-339.
  33. Xu, Y. & Zhao, J.J. & Sui, Z.N., 2010. "Exponential Runge–Kutta methods for delay differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2350-2361.
  34. Wang, Wansheng & Li, Shoufu & Wang, Wenqiang, 2009. "Contractivity properties of a class of linear multistep methods for nonlinear neutral delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 421-425.
  35. Yao, Zichen & Yang, Zhanwen & Gao, Jianfang, 2023. "Unconditional stability analysis of Grünwald Letnikov method for fractional-order delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
  36. Berezansky, Leonid & Braverman, Elena, 2019. "On stability of linear neutral differential equations in the Hale form," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 63-71.
  37. Hao Zhang, 2012. "Analysis of a Dynamic Adverse Selection Model with Asymptotic Efficiency," Mathematics of Operations Research, INFORMS, vol. 37(3), pages 450-474, August.
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