The robust numerical schemes for two-dimensional elliptical singularly perturbed problems with space shifts

References

• K. Bansal and K.K. Sharma, Parameter uniform numerical scheme for time dependent singularly perturbed convection–diffusion–reaction problems with general shift arguments, Numer. Algorithms.75(1) (2017), pp. 113–145.
   Web of Science ®Google Scholar
• C. Clavero, J. Gracia, and E. O'Riordan, A parameter robust numerical method for a two dimensional reaction–diffusion problem, Math. Comput. 74(252) (2005), pp. 1743–1758.
   Web of Science ®Google Scholar
• K.L. Cooke, Differential – difference equations, in International symposium on nonlinear differential equations and nonlinear mechanics, pp. 155–171. Elsevier, 1963 .
   Google Scholar
• R.D. Driver, Ordinary and Delay Differential Equations, Vol. 20, Springer Science & Business Media, New York, 2012.
   Google Scholar
• Garima, G. Babu, and K.K. Sharma, An ε-uniform method for singularly perturbed 2d convection dominated elliptic boundary value problems with delay and advance, Differ. Equ. Dyn. Syst. (2023), pp. 1–32.
   Web of Science ®Google Scholar
• Garima and K.K. Sharma, Parameter uniform fitted mesh finite difference scheme for elliptical singularly perturbed problems with mixed shifts in two dimensions, Int. J. Comput. Math. 100(6) (2023), pp. 1264–1283.
   Web of Science ®Google Scholar
• V.Y. Glizer, Asymptotic solution of a boundary-value problem for linear singularly-perturbed functional differential equations arising in optimal control theory, J. Optim. Theory. Appl. 106(2) (2000), pp. 309–335.
   Web of Science ®Google Scholar
• H. Han and R.B. Kellogg, Differentiability properties of solutions of the equation -ε2δu+ru=f(x,y) in a square, SIAM J. Math. Anal. 21(2) (1990), pp. 394–408.
   Web of Science ®Google Scholar
• M.K. Kadalbajoo, K.C. Patidar, and K.K. Sharma, ε-uniformly convergent fitted methods for the numerical solution of the problems arising from singularly perturbed general ddes, Appl. Math. Comput. 182(1) (2006), pp. 119–139.
   Web of Science ®Google Scholar
• M.K. Kadalbajoo and V.P. Ramesh, Hybrid method for numerical solution of singularly perturbed delay differential equations, Appl. Math. Comput. 187(2) (2007), pp. 797–814.
   Web of Science ®Google Scholar
• M.K. Kadalbajoo and K.K. Sharma, An ϵ-uniform fitted operator method for solving boundary-value problems for singularly perturbed delay differential equations: Layer behavior, Int. J. Comput. Math.80(10) (2003),pp. 1261–1276.
   Web of Science ®Google Scholar
• M.K. Kadalbajoo and K.K. Sharma, ϵ-uniform fitted mesh method for singularly perturbed differential-difference equations: mixed type of shifts with layer behavior, Int. J. Comput. Math. 81(1) (2004), pp. 49–62.
   Web of Science ®Google Scholar
• M.K. Kadalbajoo and K.K. Sharma, Numerical analysis of singularly perturbed delay differential equations with layer behavior, Appl. Math. Comput. 157(1) (2004), pp. 11–28.
   Web of Science ®Google Scholar
• C.G. Lange and R.M. Miura, Singular perturbation analysis of boundary value problems for differential-difference equations. v. small shifts with layer behavior, SIAM. J. Appl. Math. 54(1) (1994), pp. 249–272.
   Web of Science ®Google Scholar
• T. Linß and M. Stynes, A hybrid difference scheme on a shishkin mesh for linear convection–diffusion problems, Appl. Numer. Math. 31(3) (1999), pp. 255–270.
   Web of Science ®Google Scholar
• T. Linß and M. Stynes, Asymptotic analysis and shishkin-type decomposition for an elliptic convection–diffusion problem, J. Math. Anal. Appl. 261(2) (2001), pp. 604–632.
   Web of Science ®Google Scholar
• J.J.H. Miller, E. O'riordan, and G.I. Shishkin, Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions, World Scientific, Singapore, 1996.
   Google Scholar
• T.A. Nhan and R. Vulanović, The Bakhvalov mesh: A complete finite-difference analysis of two-dimensional singularly perturbed convection-diffusion problems, Numer. Algorithms. 87(1) (2021), pp. 203–221.
   Web of Science ®Google Scholar
• S.B. Norkin, Introduction to the Theory and Application of Differential Equations with Deviating Arguments, Academic Press, 1973.
   Google Scholar
• V.P. Ramesh and M.K. Kadalbajoo, Upwind and midpoint upwind difference methods for time-dependent differential difference equations with layer behavior, Appl. Math. Comput. 202(2) (2008), pp. 453–471.
   Web of Science ®Google Scholar