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摘要
The semidiscretization methods for solving the Cauchy problem (D(t)(alpha)u)(t) = Au(t) + J(1-alpha) f(t, u(t)), t is an element of [0, T], 0 < alpha < 1, u(0) = u(0), with operator A, which generates an analytic and compact resolution family {S-alpha(t, A)}(t >= 0), in a Banach space E are presented. It is proved that the compact convergence of resolvents implies the convergence of semidiscrete approximations to an exact solution. We give an analysis of a general approximation scheme, which includes finite differences and projective methods.
- 出版日期2015-4
- 单位四川大学
