Direct operatorial tau method for pantograph-type equations. The Lanczos tau method is applied to find Chebyshev polynomial approximations for the solutions of pantograph differential equations. The results are accompanied by an error analysis. Numerical examples, calculated by our Matlab package Chebpack confirm the theory and prove the importance for practice of this approach.

References in zbMATH (referenced in 15 articles , 2 standard articles )

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  1. Behera, S.; Saha Ray, S.: An efficient numerical method based on Euler wavelets for solving fractional order pantograph Volterra delay-integro-differential equations (2022)
  2. Yang, Changqing; Hou, Jianhua: Jacobi spectral approximation for boundary value problems of nonlinear fractional pantograph differential equations (2021)
  3. Rezabeyk, S.; Abbasbandy, S.; Shivanian, E.: Solving fractional-order delay integro-differential equations using operational matrix based on fractional-order Euler polynomials (2020)
  4. Zhao, Jingjun; Cao, Yang; Xu, Yang: Tau approximate solution of linear pantograph Volterra delay-integro-differential equation (2020)
  5. Ezz-Eldien, S. S.; Doha, E. H.: Fast and precise spectral method for solving pantograph type Volterra integro-differential equations (2019)
  6. Yang, Changqing: Modified Chebyshev collocation method for pantograph-type differential equations (2018)
  7. Bica, Alexandru Mihai: Initial value problems with retarded argument solved by iterated quadratic splines (2016)
  8. Bica, Alexandru Mihai; Curila, Mircea; Curila, Sorin: Two-point boundary value problems associated to functional differential equations of even order solved by iterated splines (2016)
  9. Bahşi, M. Mustafa; Çevik, Mehmet: Numerical solution of pantograph-type delay differential equations using perturbation-iteration algorithms (2015)
  10. Reutskiy, S. Yu.: A new collocation method for approximate solution of the pantograph functional differential equations with proportional delay (2015)
  11. Bhrawy, A. H.; Alghamdi, M. A.; Baleanu, D.: Numerical solution of a class of functional-differential equations using Jacobi pseudospectral method (2013)
  12. Bhrawy, A. H.; Assas, L. M.; Alghamdi, M. A.: Fast spectral collocation method for solving nonlinear time-delayed Burgers-type equations with positive power terms (2013)
  13. Bhrawy, Ali H.; Assas, Laila M.; Tohidi, Emran; Alghamdi, Mohammed A.: A Legendre-Gauss collocation method for neutral functional-differential equations with proportional delays (2013)
  14. Trif, Damian: Operatorial tau method for some delay equations (2012)
  15. Trif, Damian: Direct operatorial tau method for pantograph-type equations (2012)