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Home  >  Volume 28. No.2 (Nov. 2014)

16. A Modified Third Derivative Linear Multistep Method for Stiff ODEs by R. I. Okuonghae and N. J. Nwokorie - Volume28, No. 2, (November, 2014), pp 107 – 114
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Abstract 

Linear multistep method (LMM) is one of the traditional methods employed for the numerical solution of initial value problems (IVPs) in ordinary differential equations (ODEs). Indeed, an extension of this traditional method offers the benefit of bypassing the stability and convergence constraints imposed by the Dahlquist order barrier on LMM for ODEs. In this paper, a modified  third derivative LMM for the numerical integration of stiff systems in ODEs is presented. The methods are A( α )-stable for step number  8 ≤ k . Numerical results show that method is of good accuracy when applied to standard stiff problems. 

Keywords:

IVPs;Third derivative linear multistep methods; hybrid LMM;A( α )-stability. AMS subject classification:65L05, 65L06. 

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