دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات45
تعداد شماره‌ها1,532
تعداد مقالات18,614
تعداد مشاهده مقاله61,077,639
تعداد دریافت فایل اصل مقاله21,899,476
Conte, Dajana, Moradi, Leila, Paternoster, Beatrice. (1402). Exponentially fitted IMEX peer methods for an advection-diffusion problem. سامانه مدیریت نشریات علمی, 12(2), 287-303. doi: 10.22034/cmde.2023.53247.2248
Dajana Conte; Leila Moradi; Beatrice Paternoster. "Exponentially fitted IMEX peer methods for an advection-diffusion problem". سامانه مدیریت نشریات علمی, 12, 2, 1402, 287-303. doi: 10.22034/cmde.2023.53247.2248
Conte, Dajana, Moradi, Leila, Paternoster, Beatrice. (1402). 'Exponentially fitted IMEX peer methods for an advection-diffusion problem', سامانه مدیریت نشریات علمی, 12(2), pp. 287-303. doi: 10.22034/cmde.2023.53247.2248
Conte, Dajana, Moradi, Leila, Paternoster, Beatrice. Exponentially fitted IMEX peer methods for an advection-diffusion problem. سامانه مدیریت نشریات علمی, 1402; 12(2): 287-303. doi: 10.22034/cmde.2023.53247.2248

Exponentially fitted IMEX peer methods for an advection-diffusion problem

Computational Methods for Differential Equations
مقاله 6، دوره 12، شماره 2، خرداد 2024، صفحه 287-303    اصل مقاله (1.38 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.53247.2248
نویسندگان
Dajana Conte؛ Leila Moradi* ؛ Beatrice Paternoster
University of Salerno, Fisciano, 84084, Salerno, Italy.
چکیده
In this paper, Implicit-Explicit (IMEX) Exponential Fitted (EF) peer methods are proposed for the numerical solution of an advection-diffusion problem exhibiting an oscillatory solution. Adapted numerical methods both in space and in time are constructed. The spatial semi-discretization of the problem is based on finite differences, adapted to both the diffusion and advection terms, while the time discretization employs EF IMEX peer methods. The accuracy and stability features of the proposed methods are analytically and numerically analyzed. 
کلیدواژه‌ها
Advection-diffusion problems؛ EF IMEX peer methods؛ Boussinesq equation؛ Finite differences
مراجع
  • [1] R. Aris, On the dispersion of a solute in a fluid flowing through a tube, Proc R Soc Lond A, 235(1200) (1956), 67–77.
  • [2] U. M. Ascher, S. J. Ruuth, and R. J. Spiteri, Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations, Appl. Numer. Math., 25 (1997), 151–167.
  • [3] U. M. Ascher, S. J. Ruuth, and B. Tr. Wetton, Implicit-explicit methods for time-dependent partial differential equations, SIAM J. Numer. Anal., 32 (1995), 797–823.
  • [4] S. Beck, S. Gonzalez-Pinto, S. Perez-Rodriguez, and R. Weiner, A comparison of AMF-and Krylov-methods inmatlabfor large stiff ode systems, J. Comput. Appl. Math., 262 (2014), 292–303.
  • [5] S. Beck, R. Weiner, H. Podhaisky, and B. Schmitt, Implicit peer methods for large stiff ODE systems, Appl. Math. Comput., 38 (2012), 389–406.
  • [6] S. Boscarino, Error analysis of IMEX Runge-Kutta methods derived from differential-algebraic systems, SIAM J. Numer. Anal., 45 (2007), 1600–1621.
  • [7] S. Boscarino, On an accurate third order implicit-explicit Runge-Kutta method for stiff problems, ppl. Numer. Math., 59(7) (2009), 1515–1528.
  • [8] M. Bras, G. Izzo, and Z. Jackiewicz, Accurate implicit-explicit general linear methods with inherent Runge-Kutta stability, J. Sci. Comput., 70 (2017), 1105–1143.
  • [9] J. C. Butcher, General linear methods, Acta Numer., 15 (2006), 157–256.
  • [10] A. Cardone, R. D’Ambrosio, and B. Paternoster, Exponentially fitted IMEX methods for advection-diffusion problems, J. Comput. Appl. Math., 316 (2017), 100–108.
  • [11] A. Cardone, L. Gr. Ixaru, and B. Paternoster, Exponential fitting direct quadrature methods for Volterra integral equations, Numer. Algorithms., 55 (2010), 467–480.
  • [12] A. Cardone, L. Gr. Ixaru, B. Paternoster, and G. Santomauro, Ef-Gaussian direct quadrature methods for Volterra integral equations with periodic solution, Math. Comput. Simulat., 110(C) (2015), 125–143 .
  • [13] D. Conte, E. Esposito, L. Gr. Ixaru, and B. Paternoster, Some new uses of the ηm(Z) functions, Comput. Phys. Commun., 181 (2010), 128–137.
  • [14] A. Cardone, Z. Jackiewicz, A. Sandu, and H. Zhang, Extrapolation-based implicit-explicit general linear methods. Numer. Algor., 65 (2014), 377–399.
  • [15] A. Cardone, Z. Jackiewicz, and A. Sandu, Extrapolated Implicit-Explicit Runge-Kutta Methods. Mathematical Modelling and Analysis, 19(1) (2014), 18–43.
  • [16] D. Conte, R. D’Ambrosio, M. Moccaldi, and B. Paternoster, Adapted explicit two-step peer methods, J. Num. Math. 255 (2018) ,725–736.
  • [17] D. Conte, L. Gr. Ixaru, B. Paternoster, and G. Santomauro, Exponentially-fitted Gauss-Laguerre quadrature rule for integrals over an unbounded interval, J. Comput. Appl. Math., 255 (2014), 725–736.
  • [18] D. Conte, L. Moradi B. Paternoster, and F. Mohammadi, Construction of exponentially fitted explicit peer methods, International Journal of Circuits, Systems and Signal Processing, 13 (2019), 501–506, .
  • [19] D. Conte, F. Mohammadi, L. Moradi, and B. Paternoster, Exponentially fitted two-step peer methods for oscillatory problems, Comput. Appl. Math., 39 (2020), 10.1007/s40314-020-01202-x.
  • [20] D. Conte and B. Paternoster, Modified Gauss-Laguerre Exponential Fitting Based Formulae, J. Sc. Comp., 69(1) (2016), 227–243.
  • [21] R. D’Ambrosio, E. Esposito, and B. Paternoster, Parameter estimation in exponentially fitted hybrid methods for second order ordinary differential problems, J. Math. Chem., 50 (2012), 155–168.
  • [22] R. D’Ambrosio, E. Esposito, and B. Paternoster, Exponentially fitted two-step Runge-Kutta methods: Construction and parameter selection, Appl. Math. Comput. 218(14) (2012) 7468–7480.
  • [23] R. D’Ambrosio, M. Ferro, and B. Paternoster, Two-step hybrid collocation methods for y00 = f(x;y), Appl. Math. Lett., 22 (2009), 1076–1080.
  • [24] R. D’Ambrosio, M. Moccaldi, and B. Paternoster, Parameter estimation in IMEX-trigonometrically fitted methods for the numerical solution of reaction-diffusion problems, Computer Physics Communication., 226 (2018) 55–66.
  • [25] R. D’Ambrosio, M. Moccaldi, and B. Paternoster, Adapted numerical methods for advection-reaction-diffusion problems generating periodic wavefronts, Computers & Mathematics with Applications, Computers and Mathematics with Applications., 74(5) (2017), 1029–1042.
  • [26] R. D’Ambrosio and B. Paternoster, Numerical solution of reaction-diffusion systems of λ-ω type by trigonometrically fitted methods, J. Comput. Appl. Math., 294 (2016), 436–445 .
  • [27] R. D’Ambrosio and B. Paternoster, Exponentially fitted singly diagonally implicit Runge-Kutta methods, J. Comput. Appl. Math., 263 (2014), 277–287.
  • [28] R. D’Ambrosio and B. Paternoster, Numerical solution of a diffusion problem by exponentially fitted finite difference methods, Springer. Plus., 3 (2014), 425.
  • [29] D. R. Durran and P. N. Blossey, Implicit-explicit multistep methods for fast-wave-slow-wave problems, Mon. Weather Rev., 140 (2012), 1307–1325.
  • [30] Q. Fattah and J. Hoopes, Dispersion in anistropic homogenoeous porous media. J Hydraul Eng., 111 (1985), 810–27 .
  • [31] J. Frank, W. Hundsdorfer, and J. G. Verwer, On the stability of IMEX linear multistep methods, Appl. Numer. Math., 25 (1997), 193–205.
  • [32] A. Gerisch, J. Lang, H. Podhaisky, and R. Weiner, High-order linearly implicit two-step peer-finite element methods for time-dependent PDEs, Appl. Numer. Math., 59 (2009), 624–638.
  • [33] D. Ghosh and E. M. Constantinescu, Semi-implicit time integration of atmospheric flows with characteristic-based flux partitioning, SIAM J. Sci. Comput., 38(3) (2016) A1848–A1875.
  • [34] F. X. Giraldo, J. F. Kelly, and E. M. Constantinescu, Implicit-explicit formulations of a three-dimensional nonhydrostatic unified of the atmosphere (NUMA), SIAM J. Sci. Comput., 35(5) (2013), B1162–B1194.
  • [35] V. Guvanasen and R. Volker, Numerical solution for solute transport in unconfined aquifers, Int. J. Numer. Meth. Fluids., 3 (1983), 103–23.
  • [36] W. Hundsdorfer, and S. J. Ruuth, IMEX extensions of linear multistep methods with general monotonicity and boundedness properties, J. Comput. Phys., 225 (2007), 2016–2042.
  • [37] W. Hundsdorfer and J. Verwer, Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, in: Springer Series in Computational Mathematics, vol. 33, Springer-Verlag, Berlin, Heidelberg, 2003.
  • [38] E. Isaacson and H. B. Keller, Analysis of Numerical Methods, Dover Publications, New York, 1994.
  • [39] J. Isenberg and C. Gutfinger, Heat transfer to a draining film., Int. J. Heat. Transfer, 16 (1972), 505–12 .
  • [40] L. Gr. Ixaru and G. Vanden Berghe, Exponential Fitting, Kluwer, Boston-Dordrecht-London, 2004.
  • [41] L.Gr. Ixaru and B. Paternoster, A Gauss quadrature rule for oscillatory integrands, Comput. Phys. Commun., 133 (2001), 177–188.
  • [42] Z. Jackiewicz, General Linear Methods for Ordinary Differential Equations, John Wiley and Sons Ltd., Chichester, 2009.
  • [43] J. K. Kim, R. Cools, and L. Gr. Ixaru, Extended quadrature rules for oscillatory integrands, Appl. Numer. Math., 46 (2003), 59–73.
  • [44] J. K. Kim, R. Cools, and L. Gr. Ixaru, Quadrature rules using first derivatives for oscillatory integrands, J. Comput. Appl. Math., 140 (2002), 479–497.
  • [45] J. D. Logan and V. Zlotnik, The convection-diffusion equation with periodic boundary conditions, Appl. Math. Lett., 8(3) (1995), 55–61.
  • [46] M. A. Marino and J. N. Luthin, Seepage and Groundwater, Elsevier, Amsterdam, 1982.
  • [47] J. Y. Parlarge, Water transport in soils. Ann Rev Fluids Mech, 2 (1980), 77–102.
  • [48] B. Paternoster, Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70-th anniversary, Comput. Phys. Comm., 183 (2012), 2499–2512.
  • [49] H. Podhaisky, R. Weiner, and B. Schmitt, Rosenbrock-type ‘Peer’ two-step methods, Appl. Numer. Math., 53 (2005), 409–420.
  • [50] S. J. Ruuth, Implicit-explicit methods for reaction-diffusion problems in pattern formation, J. Math. Biol., 34 (1995), 148–176.
  • [51] J. R. Salmon, J. A. Ligett, and R. H. Gallager, Dispersion analysis in homogeneous lakes, Int. J. Numer. Meth. Eng., 15 (1980), 1627–42.
  • [52] W. E. Schiesser, The Numerical Method of Lines: Integration of Partial Differential Equations, Academic Press, San Diego, 1991.
  • [53] W. E. Schiesser and G. W. Griffiths, A Compendium of Partial Differential Equation Models: Method of Lines Analysis with Matlab, Cambridge University Press, 2009.
  • [54] B. A. Schmitt, R. Weiner, and K. Erdmann, Implicit parallel peer methods for stiff initial value problems, Appl. Numer. Math., 53 (2005), 457–470.
  • [55] B. A. Schmitt, R. Weiner, and H. Podhaisky, Multi-implicit peer two-step W-methods for parallel time integration, BIT Numer. Math., 45 (2005), 197–217.
  • [56] T. E. Simos, A fourth algebraic order exponentially-fitted Runge-Kutta method for the numerical solution of the Schr¨odinger equation, IMA Journ. of Numerical Analysis, 21 (2001), 919–931.
  • [57] K. M. Singh and M. Tanaka, On exponential variable transformation based boundary element formulation for advection-diffusion problems, Eng. Anal. Bound. Elem., 24 (2000), 225–35.
  • [58] G. D. Smith, Numerical Solution of Partial Differential Equations-Finite Difference Methods, Clarendon Press, Oxford, 1985.
  • [59] B. Soleimani, O. Knothb, and R. Weiner, IMEX peer methods for fast-wave-slow-wave problems, App. Num. Math., 118 (2017), 221–237.
  • [60] B. Soleimani and R. Weiner, A class of implicit peer methods for stiff systems, J. Comput. Appl. Math., 316 (2017), 358–368.
  • [61] N. Su, F. Liu, and V. Anh, Tides as a phase modulated waves inducing periodic groundwater flow in coastal aquifers overlaying a sloping impervious base, Environ. Model. Softw., 18 (2003), 937–942.
  • [62] M. Van Daele, G. Vanden Berghe, and H. Vande Vyver, Exponentially fitted quadrature rules of Gauss type for oscillatory integrands, Appl. Numer. Math., 53 (2005), 509–526.
  • [63] G. Vanden Berghe, L. Gr. Ixaru, and M. Van Daele, Optimal implicit exponentially-fitted Runge–Kutta methods, Comput. Phys. Commun., 140 (2001), 346–357.
  • [64] H. Wang, C. W. Shu, and Q. Zhang, Stability and error estimates of local discontinuous galerkin methods with implicit-explicit time-marching for advection-diffusion problems, SIAM J. Numer. Anal., 53(1) (2015), 206–227.
  • [65] R. Weiner, K. Biermann, B. A. Schmitt, and H. Podhaisky, Explicit two-step peer methods, Comput. Math. Appl., 55(4) (2008), 609–619.
  • [66] R. Weiner, B. A. Schmitt, H. Podhaisky, and S. Jebens, Superconvergent explicit two-step peer methods, J. Comput. Appl. Math., 223 (2009), 753–764.
  • [67] P. W. Werner, Some problems in non-artesian ground-water flow, Trans. Amer. Geophys. Union., 38(4) (1958), 511–558.
  • [68] H. Zhang, A. Sandu, and S. Blaise, Partitioned and implicit–explicit general linear methods for ordinary differential equations, J. Sci. Comput., 61 (2014), 119–144.
  • [69] E. Zharovsky, A. Sandu, and H. Zhang, A class of implicit-explicit two-step Runge-Kutta methods, SIAM J. Numer. Anal., 53 (2015), 321–341.
  • [70] Z. Zlatev, R. Berkowicz, and L. P. Prahm, Implementation of a variable stepsize variable formula in the timeintegration part of a code for treatment of long-range transport of air pollutants., J Comp Phys, 55 (1984), 278–301.
آمار
تعداد مشاهده مقاله: 452
تعداد دریافت فایل اصل مقاله: 673


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب