Abstract
A class of one-step finite difference formulae for the numerical solution of first-order differential equations is considered. The accuracy and stability properties of these methods are investigated. By judicious choice of the coefficients in these formulae a method is derived which is both A-stable and third-order convergent. Moreover the new method is shown to be L-stable and so is appropriate for the solution of certain stiff equations. Numerical results are presented for several test problems.
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