A stable finite difference approximation for vibration equation of beams 梁振動方程的一個穩(wěn)定的有限差分近似
( 5 ) discuss some mathematical models of the pollutant transport problems in some local river flow fields . by integral transform method , the paper establishes the usual finite difference approximation scheme to solve the numerical solutions and gives examples for the computation of the approximating solutions , moreover , discusses one - dimensional characteristic finite difference method for a convection - diffusion equation under usual conditions ( 5 )針對水域中污染物輸移問題的數(shù)學模型,通過積分變換法,得到了簡化模型在理想化條件下的近似精確解,同時給出數(shù)值算例,并且對非理想化條件下模型的特征差分方法進行了討論。
It is proposed on the basis of the analysis on newton method and the preconditioned conjugate gradient method ( pcg method ) . numerical derivatives can be evaluated by symbolic differ - entiation ( sd ) , finite difference approximation and automatic differelltiation ( ad ) . ad has significant advantages over other two approaches 自動微分是一種新的能精確而有效地計算導數(shù)的方法,它優(yōu)越于傳統(tǒng)的微分方法,例如它比符號微分和差分方法的計算成本低,又比差分方法計算精確,自動微分在近幾年發(fā)展迅速,應用廣泛。