摘要
提出了附属于非线性算子 Ａ的半范数 Ａ 及微分方程式的广义解算子 Ｅ 的概 念与性质，并引入非线性差分逼近的相容性、收敛性、稳定性概念。利用这些概念，证明 了非线性微分方程的初值问题差分逼近的等价性定理。最后说明了常微分方程数值解 的收敛性定理即本定理的特例。
This paper gives the conceptions of consistency, convergence, stability, seminorm of an operator of the nonlinear difference approximation and the Lax's equivalence theorem to the non-linear case. Equivalence theorem: Giving a properly posed non-linear initial-value problem and a nonlinear finite-difference approximation that satisfies the consistency conditions, then stability is necessary and sufficient conditions for convergence.
出处
《大连理工大学学报》
EI
CAS
CSCD
北大核心
1989年第3期259-264,共6页
Journal of Dalian University of Technology
关键词
差分
逼近
非线性
等价
稳定性
difference
approximation
non-linear
consistency (mathematics)
convergence
stability (mathematics)
equivalence
