论文信息 - Exact finite difference and non-standard finite difference schemes for

Exact finite difference and non-standard finite difference schemes for

Exact finite difference schemes and non-standard finite difference schemes are constructed for the first-order differential equation , for and . In particular, we show that the central finite difference scheme is an exact scheme for the differential equation .

Ronald E. Mickens | Lih-Ing W. Roeger

[1] Ronald E. Mickens,et al. Finite-difference schemes having the correct linear stability properties for all finite step-sizes III , 1994 .

[2] Shigehiro Ushiki,et al. Central difference scheme and chaos , 1982 .

[3] Non-standard finite difference schemes for the differential equation y′(t)=b n y n +b n−1 y n−1+…+b 1 y+b 0 , 2012 .

[4] Lih-Ing W. Roeger. Nonstandard finite difference schemes for differential equations with n+1 distinct fixed-points , 2009 .

[5] R. Mickens. Nonstandard Finite Difference Models of Differential Equations , 1993 .

[6] Roger W. Barnard,et al. Preservation of local dynamics when applying central difference methods: application to SIR model , 2007 .

[7] Shigehiro Ushiki,et al. Chaos in numerical analysis of ordinary differential equations , 1981 .

[8] F. B. Hildebrand. Finite-difference equations and simulations , 1968 .

[9] A. Pankov,et al. Differential and Difference Equations , 2020 .

[10] Ronald E. Mickens,et al. Advances in the Applications of Nonstandard Finite Difference Schemes , 2005 .

[11] J. M. Sanz-Serna,et al. Studies in Numerical Nonlinear Instability I. Why do Leapfrog Schemes Go Unstable , 1985 .