An almost L‐stable BDF‐type method for the numerical solution of stiff ODEs arising from the method of lines

A new BDF-type scheme is proposed for the numerical integration of the system of ordinary differential equations that arises in the Method of Lines solution of time-dependent partial differential equations. This system is usually stiff, so it is desirable for the numerical method to solve it to have good properties concerning stability. The method proposed in this article is almost L-stable and of algebraic order three. Numerical experiments illustrate the performance of the new method on different stiff systems of ODEs after discretizing in the space variable some PDE problems. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007

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