O numeričkom rješavanju Cauchyjevog problema Runge-Kutta metodama na Shishkinovoj mreži Stručno-istraživački rad
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Nov 6, 2023
Ključne riječi:
Cauchyjev problem, Runge–Kutta metode, slojno-adativne mreže
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Sažetak
U ovom radu razmatrano je numeričko rješavanje singularno–perturbacionog Cauchyjevog problema Runge–Kutta metodama na Shishkinovoj mreži. Numerička rješenja posmatranog problema dobijena su korištenjem dvije eksplicitne i jedne implicitne Runge–Kutta metode na najjednostavnijoj slojno–adaptivnoj mreži. Na kraju su dobijeni rezultati uporedeni.
Ciljna skupina: fakultet
Rad preuzet: 2023.
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[1]
Vesna Divković, Laura Lukić, Elvir Memić, i Samir Karasuljić, O numeričkom rješavanju Cauchyjevog problema Runge-Kutta metodama na Shishkinovoj mreži, Evolventa, vol. 6, no. 1 (2023), 33-46.
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[3] W. Kutta, Beitrag zur n¨aherungsweisen Integration totaler Differentialgleichungen, Zeit. Math. Phys., Vol.46, pp 435-453, 1901.
[4] V. D. Liseikin, Layer Resolving Grids and Transformations for Singular Perturbation Problems, VSP BV, AH Zeist, The Netherlands, 2001.
[5] V. D. Liseikin, Grid Generation for Problems with Boundary and Interior Layers, Novosibirsk State University, Novosibirsk, 2018.
[6] V. D. Liseikin, S. Karasuljić, and V. I. Paasonen, Numerical Grids and High-Order Schemes for Problems with Boundary and Interior Layers, Novosibirsk State University, Novosibirsk, 2021.
[7] V. D. Lisejkin and V. E. Petrenko, The adaptive-invariant method for the numerical solution of problems with boundary and interior layers, Novosibirsk: Vychislitel’nyj Tsentr SO AN SSSR, 1989.
[8] C. Runge, Ueber die numerische Aufl¨osung von Differentialgleichungen, Zenodo, 1895.
[9] G. I. Shishkin, Grid approximation of singularly perturbed parabolic equations with internal layers, Sov. J. Numer. Anal. M.Russian Journal of Numerical Analysis and Mathematical Modelling, Vol 3(5), pp 393-408, 1988.
[10] R. Vulanović, Mesh construction for discretization of singularly perturbed boundary value problems, Univerzitet u Novom Sadu, 1986.