解刚性常微分方程组L-稳定的显式单步法及数值试验

L-Stable Explicit One-Step Method for Solving Stiff Ordinary Differential Equation and Its Numerical Experiments

给出了求解试验方程组 y′=Λ y,Λ=diag( λ1,λ2 ,… ,λm) ,Re( λi) <0 ,i=1,2 ,… ,m,m为任意整数的 L-稳定的显式单步法 ,对上述方程组它是完全精确的 .但对一般方程组精度不高 ,于是又给出了另一个 L-稳定的 3阶显式单步法 ,此方法适用于线性的。

For solving stiff systems a L\|stable explicit one\|step method is given ,it is completely accurate to text equations y\+′=Λy,Λ=diag(λ\-1,λ\-2,…,λ\-m),Re(λ\-i)<0,i=1,2,…,m∈Z\++.But it is not accurate enough to others, so we give another L\|stable explicit one\|step method of order 3.The numerical experiments shows that the method is effective for linear ,non\|linear stiff systems.