Euler approximations can destroy unbounded solutions

• Autorzy: Guy, R. T. , Misiurewicz, M.
• Języki publikacji: EN

Abstrakty

EN

We show that there are ordinary differential equations in R^d with unbounded solutions, for which the difference equations obtained by using the forward Euler method have all solutions bounded.

Słowa kluczowe

PL

równania różniczkowe; wzór Eulera

EN

Euler method; differential equations; difference equations; unbounded solutions

• Czasopismo: Fasciculi Mathematici
• Rocznik: 2010
• Tom: Nr 44
• Strony: 43-52
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Guy, R. T.

autor

Misiurewicz, M.

• Department of Mathematical Sciences Indiana University - Purdue University Indianapolis 402 N. Blackford Street, Indianapolis, IN 46202, USA,

Bibliografia

• [1] Berger U., Hofbauer J., The Nash dynamics, preprint, 1996.
• [2] Geller W., Kitchens B., Misiurewicz M., Microdynamics for Nash maps, Discrete Contin. Dynam. Sys, 27(2010), 1007-1024.
• [3] Hofbauer J., Iooss G., A Hopf bifurcation theorem for difference equations approximating a differential equation, Monatsh. Math., 98(1984), 99-113.
• [4] Li M.-C., Structural stability for the Euler method, SIAM J. Math. Anal., 30(1999), 747-755.
• [5] Mikołajski J., Schmeidel E., Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients), Opuscula Math., 26(2006), 343-349.
• [6] Roeger L.-I.W., Local stability of Euler’s and Kahan’s methods, J. Difference Equ. Appl., 10(2004), 601-614.
• [7] Shampine L.F., Numerical Solution of Ordinary Differential Equations, Chapman and Hall, New York, 1994.
• [8] Walter W., Ordinary Differential Equations, Springer, New York, 1998.