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Numerical Methods for Delay Differential Equations

Citations

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Cited by:

  1. Gui-Lai Zhang & Zhi-Yong Zhu & Yu-Chen Wang & Chao Liu, 2024. "Impulsive Discrete Runge–Kutta Methods and Impulsive Continuous Runge–Kutta Methods for Nonlinear Differential Equations with Delayed Impulses," Mathematics, MDPI, vol. 12(19), pages 1-30, September.
  2. Wei Gu, 2014. "A Compact Difference Scheme for a Class of Variable Coefficient Quasilinear Parabolic Equations with Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
  3. 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.
  4. Haiyan Yuan & Jingjun Zhao & Yang Xu, 2012. "Some Stability and Convergence of Additive Runge‐Kutta Methods for Delay Differential Equations with Many Delays," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
  5. 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.
  6. Dongfang Li & Chao Tong & Jinming Wen, 2014. "Stability of Exact and Discrete Energy for Non‐Fickian Reaction‐Diffusion Equations with a Variable Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
  7. 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.
  8. 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).
  9. 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.
  10. 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.
  11. Wansheng Wang & Shoufu Li, 2012. "On the One‐Leg Methods for Solving Nonlinear Neutral Differential Equations with Variable Delay," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
  12. Zhan, Rui & Fang, Jinwei, 2024. "Stability analysis of explicit exponential Rosenbrock methods for stiff differential equations with constant delay," Applied Mathematics and Computation, Elsevier, vol. 482(C).
  13. A. H. Bhrawy & M. A. Alghamdi & D. Baleanu, 2013. "Numerical Solution of a Class of Functional‐Differential Equations Using Jacobi Pseudospectral Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
  14. 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.
  15. 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.
  16. G. L. Zhang & M. H. Song & M. Z. Liu, 2012. "Asymptotic Stability of a Class of Impulsive Delay Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
  17. 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.
  18. 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.
  19. Deng, Shuning & Ji, Jinchen & Wen, Guilin & Yin, Shan, 2024. "Global dynamics of a hexagonal governor system with two time delays in the parameter and state spaces," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
  20. 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.
  21. 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.
  22. Z. I. Ismailov & P. Ipek, 2014. "Spectrums of Solvable Pantograph Differential‐Operators for First Order," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
  23. 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).
  24. 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.
  25. V. G. Pimenov & A. S. Hendy, 2015. "Numerical Studies for Fractional Functional Differential Equations with Delay Based on BDF‐Type Shifted Chebyshev Approximations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
  26. 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.
  27. 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.
  28. 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.
  29. 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.
  30. 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.
  31. 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.
  32. Gambaro, Nicola & Brito-Parada, Pablo & Glöser-Chahoud, Simon & Plancherel, Yves, 2025. "Simulating resource movements and markets: A continuous dynamical system with delays to model anthropogenic metal cycles," Resources Policy, Elsevier, vol. 103(C).
  33. 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.
  34. Wei Gu & Ming Wang & Dongfang Li, 2014. "Stepsize Restrictions for Nonlinear Stability Properties of Neutral Delay Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
  35. 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).
  36. Wang, Qi, 2015. "Numerical oscillation of neutral logistic delay differential equation," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 49-59.
  37. 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.
  38. 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.
  39. 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.
  40. Yang, Yin & Yao, Pai & Tohidi, Emran, 2026. "A high accurate numerical framework for the solution of the vanishing-delay Volterra integro-differential equations via Legendre pseudo-spectral element approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 240(C), pages 403-422.
  41. Ashwin Aravindakshan & Prasad A. Naik, 2015. "Understanding the Memory Effects in Pulsing Advertising," Operations Research, INFORMS, vol. 63(1), pages 35-47, February.
  42. 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.
  43. 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.
  44. 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.
  45. 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.
  46. 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.
  47. 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.
  48. 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).
  49. 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.
  50. Haiyan Yuan & Jingjun Zhao & Yang Xu, 2012. "Nonlinear Stability and D‐Convergence of Additive Runge‐Kutta Methods for Multidelay‐Integro‐Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
  51. Behroozi, Hasan & Kazemi, Manochehr & Ezzati, Reza, 2025. "Successive approximations method is used to solve nonlinear Volterra delay integral equations," Applied Mathematics and Computation, Elsevier, vol. 507(C).
  52. 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.
  53. 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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