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Articles

Uniform difference method for singularly pertubated delay Sobolev problems

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Pages 1713-1736 | Received 17 Jan 2019, Published online: 26 Sep 2019

References

  • I. Amirali, G.M. Amiraliyev, M. Cakir, and E. Cimen, Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations, The Scientific World Journal, 2014 (2014), Article ID 497393.
  • G.M. Amiraliyev, Investigation of the Difference Schemes for the Quasi-Linear Sobolev Equations, Differential Equations 23(8) (1987), 1453–1455.
  • G.M. Amiraliyev, Difference Method for the Solution of One Problem of the Theory of Dispersive Waves, Differential Equations 26 (1990), 2146–2154.
  • G.M. Amiraliyev, Difference Schemes on the Uniform Mesh for Singular Perturbed Pseudo-Parabolic Equation, Turkish J. of Math. 19 (1995), 207–222.
  • G.M. Amiraliyev and E. Cimen, Numerical method for a singularly perturbed convection–diffusion problem with delay, Applied Mathematics and Computation 216 (2010), 2351–2359.
  • G.M. Amiraliyev, E. Cimen, I. Amirali, and M. Cakir, High-Order Finite Difference Technique for Delay Pseudo-Parabolic Equations, J. of Com. and Appl. Math. 321 (2017), 1–7.
  • G.M. Amiraliyev, H. Duru, and I. Amiraliyeva, A Parameter-uniform Numerical Method for a Sobolev Problem with Initial Layer, Numer. Algor. 44 (2007), 185–203.
  • 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. of Comput. and App. Math. 205(1) (2007), 552–566.
  • K. Bansal and K.K. Sharma, Parameter-Robust Numerical Scheme for Time-Dependent Singularly Perturbed Reaction–Diffusion Problem with Large Delay, Numerical Functional Analysis and Optimization 39(2) (2018), 127–154.
  • R.K. Bullough and P.J. Caudrey, Solitons, Springer-Verlag, New York, 1980.
  • E. Cimen, Numerical Solution of a Boundary Value Problem Including Both Delay and Boundary Layer, Mathematical Modelling and Analysis 23(4) (2018), 568–581.
  • E.P. Doolan, J.J. Miller, and W.H.A. Schilders, Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole Press, Dublin, 1980.
  • H. Duru, Difference schemes for the singularly perturbed Sobolev periodic boundary problem, Applied Mathematics and Computation 149 (2004), 187–201.
  • F. Erdogan, An Exponentially Fitted Method for Singularly Perturbed Delay Differential Equations, Advances in Difference Equations 2009 (2009), Article ID 781579.
  • R.E. Ewing, Time Stepping Galerkin Methods for Nonlinear Sobolev Partial Differential Equations, SIAM J.Numer Anal. 15 (1978), 1125–1150.
  • W.E. Ford and T.W. Ting, Uniform Error Estimates for Difference Approximations to Nonlinear Pseudo-Parabolic Partial Differential Equations, SIAM J. Numer. Anal. 11 (1974), 155–169.
  • F. Ghomanjani, A. Kılıçman, and F. Akhavan Ghassabzade, Numerical Solution of Singularly Perturbed Delay Differential Equations with Layer Behavior, Abstract and Applied Analysis 2014 (2014), Article ID 731057.
  • H. Ikezi, Experiments on Solitons in Plasmas, Solitons in Action, K. Lonngren and A. Scott, eds., Academic Press, New York, 1978.
  • M.K. Kadalbajoo and Y.N. Reddy, Asymptotic and Numerical Analysis of Singular Perturbation Problems, A survey, App. Math. And Comput. 30 (1989), 223–259.
  • M.K. Kadalbajoo and A.S. Yadaw, Parameter-Uniform Finite Element Method for Two-Parameter Singularly Perturbed Parabolic Reaction-Diffusion Problems, Int. J. of Comp. Methods 9 (2012), No. 41250047.
  • J.L. Langnese, General Boundary-Value Problems for Differential Equations of Sobolev Type, SIAM J. Math. Anal. 3 (1972), 105–119.
  • V.I. Lebedev, The Method of Difference for the Equations of Sobolev Type, Dokl. Acad. Sci. USSR 114(6) (1957), 1166–1169.
  • K.E. Lonngren, Observation of Solitons on Nonlinear Dispersive Transmission Lines, Soliton in Action, Academic Press, New York, 1978.
  • A.A. Samarskii, Theory of Difference Schemes, 2 ed., Nauka, Moscow, 1983.
  • C.L. Sobolev, On a new problem of mathematical physics, Izv. Akad. Nauk SSSR Ser. Mat. 18(1) (1954), 3–50.
  • J. Wu, Theory and Applications of Partial Functional Differential Equations, Springer-Verlag, New York, 1996.

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