刊名:Journal of Computational and Applied Mathematics
出版年:2017
出版时间:15 March 2017
年:2017
卷:313
期:Complete
页码:284-293
全文大小:402 K
文摘
If a spectral numerical method for solving ordinary or partial differential equations is written as a biinfinite linear system b=Za with a map that has a continuous inverse, this paper shows that one can discretize the biinfinite system in such a way that the resulting finite linear system is uniquely solvable and is unconditionally stable, i.e. the stability can be made to depend on Z only, not on the discretization. Convergence rates of finite approximations of b then carry over to convergence rates of finite approximations of a. Spectral convergence is a special case. Some examples are added for illustration.