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Sahu, Subal, Mohapatra, Jugal, Govindarao, Lolugu. (1402). A second order numerical scheme for solving mixed type boundary value problems involving singular perturbation. سامانه مدیریت نشریات علمی, 11(4), 822-833. doi: 10.22034/cmde.2023.52094.2178
Subal Ranjan Sahu; Jugal Mohapatra; Lolugu Govindarao. "A second order numerical scheme for solving mixed type boundary value problems involving singular perturbation". سامانه مدیریت نشریات علمی, 11, 4, 1402, 822-833. doi: 10.22034/cmde.2023.52094.2178
Sahu, Subal, Mohapatra, Jugal, Govindarao, Lolugu. (1402). 'A second order numerical scheme for solving mixed type boundary value problems involving singular perturbation', سامانه مدیریت نشریات علمی, 11(4), pp. 822-833. doi: 10.22034/cmde.2023.52094.2178
Sahu, Subal, Mohapatra, Jugal, Govindarao, Lolugu. A second order numerical scheme for solving mixed type boundary value problems involving singular perturbation. سامانه مدیریت نشریات علمی, 1402; 11(4): 822-833. doi: 10.22034/cmde.2023.52094.2178

A second order numerical scheme for solving mixed type boundary value problems involving singular perturbation

Computational Methods for Differential Equations
مقاله 12، دوره 11، شماره 4، مهر 2023، صفحه 822-833    اصل مقاله (376.4 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.52094.2178
نویسندگان
Subal Ranjan Sahu1؛ Jugal Mohapatra* 2؛ Lolugu Govindarao3
1Department of Mathematics, Larambha college, Bargarh, Orissa - 768102, India.
2Department of Mathematics, National Institute of Technology Rourkela, Odisha, India.
3Department of Mathematics Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore- 641112, India.
چکیده
A class of singularly perturbed mixed type boundary value problems is considered here in this work. The domain is partitioned into two subdomains. Convection-diffusion and reaction-diffusion problems are posed on the first and second subdomain, respectively. To approximate the problem, a hybrid scheme which consists of a  second-order central difference scheme and a midpoint upwind scheme is constructed on Shishkin-type meshes. We have shown that the proposed scheme is second-order convergent in the maximum norm which is independent of the perturbation parameter. Numerical results are illustrated to support the theoretical findings.
کلیدواژه‌ها
Singular perturbation؛ Mixed problem؛ Bakhvalov-Shishkin mesh؛ Hybrid scheme؛ Uniform convergence
مراجع
  • [1] G. M. Amiraliyev, I. G. Amiraliyeva, and M. Kudu, A numerical treatment for singularly perturbed differential equations with integral boundary condition, Appl. Math. Comput., 185 (2007), 574–582.
  • [2] N. S. Bakhvalov, On the optimization of the methods for solving boundary value problems in the presence of a boundary layer, Zh. Vychisl. Mat. Mat. Fiz., 9(4) (1969), 841–859.
  • [3] I. A. Brayanov, Numerical solution of a mixed singularly perturbed parabolic-elliptic problem, J. Math. Anal. Appl., 320(1) (2006), 361–380.
  • [4] I. A. Brayanov, Uniformly convergent difference scheme for singularly perturbed problem of mixed type, Electron. T. Numer. Ana., 23 (2006), 288–303.
  • [5] M. Cakir, I. Amirali, M. Kudu, and G. M. Amiraliyev, Convergence analysis of the numerical method for a singularly perturbed periodical boundary value problem, J. Math. Computer Sci., 16 (2016), 248–255.
  • [6] P. A. Farrell, A. F. Hegarty, J. J. H. Miller, E. O’ Riordan, and G. I. Shishkin, Robust Computational Techniques for Boundary Layers, Chapman and Hall/CRC Press, New York, 2000.
  • [7] L. Govindarao and J. Mohapatra, A second order numerical method for singularly perturbed delay parabolic partial differential equation, Eng. Comput., 36(2) (2019), 420–444.
  • [8] L. Govindarao and J. Mohapatra, Numerical analysis and simulation of delay parabolic partial differential equa- tion, Eng. Comput., 37(1) (2019), 289–312.
  • [9] L. Govindarao and J. Mohapatra, A second order weighted numerical scheme on non-uniform meshes for con- vection diffusion parabolic problems, European J. Comput. Mech., 28(5) (2019), 467–498.
  • [10] L. Govindarao and J. Mohapatra, A numerical scheme to solve mixed parabolic-elliptic problem involving singular perturbation, Int. J. Comput. Math., (2022).
  • [11] R. B. Kellogg and A. Tsan, Analysis of some difference approximations for a singular perturbation problem without turning points, Math. Comput., 32(144) (1978), 1025–1039.
  • [12] M. Kudu, I. Amirali, and G. M. Amiraliyev, A layer analysis of parameterized singularly perturbed boundary value problems Int. J. Appl. Math., 29(4) (2016), 439–449.
  • [13] K. Kumar, P. C. Podila, P. Das, and H. Ramos, A graded mesh refinement approach for boundary layer originated singularly perturbed time-delayed parabolic convection diffusion problems, Math. Methods Appl. Sci., 148 (2020), 79–97.
  • [14] T. Linß, Sufficient conditions for uniform convergence on layer-adapted grids, Appl. Numer. Math., 37(1-2) (2001), 241–255.
  • [15] J. J. H. Miller, E. O’Riordan and G. I. Shishkin, Fitted Numerical Methods for Singular Perturbation Problems, World Scientific Co, Singapore, 2012.
  • [16] J. J. H. Miller, E. O’Riordan, G. I.Shishkin and S. Wang, A parameter-uniform Schwarz method for a singularly perturbed reaction diffusion problem with an interior layer, Appl. Numer. Math., 35(4) (2000), 323–337.
  • [17] J. Mohapatra and S. Natesan, Parameter-uniform numerical methods for singularly perturbed mixed boundary value problems using grid equidistribution, J. Appl. Math. Comput., 37(1) (2011), 247–265.
  • [18] K. Mukherjee and S. Natesan, Uniform convergence analysis of hybrid numerical scheme for singularly perturbed problems of mixed type, Numer. Meth. Partial Differ. Equ., 30(6) (2014), 1931–1960.
  • [19] R. E. O’Malley, Introduction to Singular Perturbations, Academic press, New York, 1974.
  • [20] R. M. Priyadharshini, N. Ramanujam, and T. Valanarasu, Hybrid difference schemes for singularly perturbed problem of mixed type with discontinuous source term, J. Appl. Math. Inf., 28(5) (2010), 1035–1054.
  • [21] N. Raji Reddy and J. Mohapatra, An efficient numerical method for singularly perturbed two point boundary value problems exhibiting boundary layers, Natl. Acad. Sci. Lett., 38 (2015), 355–359.
  • [22] H. G. Roos and H. Zarin, A second-order scheme for singularly perturbed differential equations with discontinuous source term, J. Numer. Math., 10(4) (2002), 275-289.
  • [23] S. R. Sahu and J. Mohapatra, A second-order finite difference scheme for singularly perturbed initial value problem on layer-adapted meshes, Int. J. Model. Simul. Sci. Comput., 10(3) (2019), 1950016.
  • [24] S. R. Sahu and J. Mohapatra, Numerical investigation for solutions and derivatives of singularly perturbed initial value problems, Int. J. Math. Model. Numer. Opt., 11(2) (2021), 123–142.
  • [25] D. Shakti and J. Mohapatra, A second order numerical method for a class of parameterized singular perturbation problems on adaptive grid, Nonlinear Engineering, 6(3) (2017), 221–228.
  • [26] M. Stynes and H. G. Roos, The midpoint upwind scheme, Appl. Numer. Math., 23(3) (1997), 361–374.
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