Linear stability of stiff differential equation solvers
When a linear multistep method is used to solve a stiff differential equationy′(x)=f(y(x)), producing an approximationy n toy(x n ), it is preferable to approximate the valuey′(x n ) in subsequent formulae by a value which exactly satisfies the corrector equation used, rather than by the valuef(y n ). We prove that the resulting method is stable if the underlying corrector equation is absolutely stable, provided that the residuals obtained in solving successive nonlinear equations remain uniformly bounded.
KeywordsDifferential Equation Computational Mathematic Nonlinear Equation Linear Stability Multistep Method
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