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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.
In this paper, the numerical solution of the singular-perturbation Cauchy problem by Runge-Kutta methods on the Shishkin grid is discussed. Numerical solutions of the observed problem were obtained using two explicit and one implicit Runge-Kutta method on the simplest layer-adaptive network. Finally, the obtained results were compared.
In this paper we consider two difference schemes for numerical solving of a one--dimensional singularly perturbed boundary value problem. We proved an $\varepsilon$--uniform convergence for both difference schemes on a Shiskin mesh. Finally, we present four numerical experiments to confirm the theoretical results.
