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General linear methods for ordinary differential equations

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  • Butcher, John

Abstract

General linear methods were introduced as the natural generalizations of the classical Runge–Kutta and linear multistep methods. They have potential applications, especially for stiff problems. This paper discusses stiffness and emphasises the need for efficient implicit methods for the solution of stiff problems. In this context, a survey of general linear methods is presented, including recent results on methods with the inherent RK stability property.

Suggested Citation

  • Butcher, John, 2009. "General linear methods for ordinary differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(6), pages 1834-1845.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:6:p:1834-1845
    DOI: 10.1016/j.matcom.2007.02.006
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