解刚性问题的一类指数拟合方法

An Exponentially Fitted Method for Solving Stiff Differential Equations

提出一类通过变量代换Y(x)=e^((x-x_r)L)y(x)构建的指数拟合的方法求解刚性问题.对标量模型方程y′=λy,Re(λ)<0,这类变量代换的方法具有精确指数拟合的特点.理论分析和数值试验证明,在不降低原有积分方法相容性的前提下,将该代换用于普通的数值算法之后,能取得比普通的数值算法更好的收敛性,稳定性及计算精度.

In this paper,an exponentially fitted melthod for solving stiff ordinary differential equations is derived by applying variable substitution Y(x)=e^((x-x_r)L)y(x).The method is exact exponentially fitted when applied to the test equation y'=λy with Re(λ)<0,whereλis any complex number.Theoretical analysis and numerical results indicate that,in the case of keeping the consistence of the normal integral method,the substituted method has better convergence,stability and computational accuracy than the normal integral method.