奇性常微分方程差分解的外推

本文利用 Crank—Nicholson 格式导出奇性微分方程,形如t∈0,1],0<β<1,F(t)∈C~∞0,1],F(0)≠0的差分解展开式,并对其展开式应用 Richardson 外推,使外推后的近似解(f)与真解 U(t)的误差在\{0}上达到 O(π~(2+β)).

Extrapolation of Difference Solutions to the Ordinary Differential Equations of Singularities

In this paper,the expansion equations of the difference solutions to the differential equations in the form of t0,1] 0<β<1,F(t)∈0,1],F(0)≠0 with singular solutions are derived from the Crank-Nicholson scheme,with expansions of the difference solutions by means of Richardson's extrapolation,thus keeping the errors between the approximative valus (t)resulting from extrapolation and the true value U(t) to 0(τ~(2+β)) at the points of \{0}.