Deals with the application of Kreiss resolvent condition in the error growth analysis of numerical methods, and studies the stability of Runge Kutta method in respect of Kreiss resolvent condition with emphasis on the...Deals with the application of Kreiss resolvent condition in the error growth analysis of numerical methods, and studies the stability of Runge Kutta method in respect of Kreiss resolvent condition with emphasis on the study on the subclass of collocation methods with abscissas in [0,1] by applying the methods to the test equation U′(t)=λU(t)+μU(t-τ)τ>0 with complex constraints μ and λ, and proves under some assumptions on the R K methods that the error growth is uniformly bounded in the stability region.展开更多
The stability analysis of linear multistep (LM) methods is carried out under Kreiss resolvent condition when they are applied to neutral delay differential equations of the form y′(t)=ay(t)+by(t-τ)+ cy′(t- τ) y(t)...The stability analysis of linear multistep (LM) methods is carried out under Kreiss resolvent condition when they are applied to neutral delay differential equations of the form y′(t)=ay(t)+by(t-τ)+ cy′(t- τ) y(t)=g(t) -τ≤t≤0 with τ>0 and a, b and c∈, and it is proved that the ‖B n‖ is suitably bounded, where B is the companion matrix.展开更多
文摘Deals with the application of Kreiss resolvent condition in the error growth analysis of numerical methods, and studies the stability of Runge Kutta method in respect of Kreiss resolvent condition with emphasis on the study on the subclass of collocation methods with abscissas in [0,1] by applying the methods to the test equation U′(t)=λU(t)+μU(t-τ)τ>0 with complex constraints μ and λ, and proves under some assumptions on the R K methods that the error growth is uniformly bounded in the stability region.
文摘The stability analysis of linear multistep (LM) methods is carried out under Kreiss resolvent condition when they are applied to neutral delay differential equations of the form y′(t)=ay(t)+by(t-τ)+ cy′(t- τ) y(t)=g(t) -τ≤t≤0 with τ>0 and a, b and c∈, and it is proved that the ‖B n‖ is suitably bounded, where B is the companion matrix.
