A-Stable Order Eight Second Derivative Linear Multistep Methods for Solutions of Stiff Systems of Ordinary Differential Equations (ODEs)
Keywords:
A Stability, Blended Linear Multistep Methods, Adams Methods, Backward Differentiation Method (BDF), Stiff ODEs, MSC Numerical MathematicsAbstract
In this study, accurate and efficient numerical methods with good stability properties shall be developed. The formulation of the block second derivative Blended Linear Multistep methods for step numbers k=7 is considered. The main methods are derived by blending of two methods by continuous collocation approach. These methods are of uniform order eight. With this approach, we hope to improve the stability regions of the Adams Moultons Methods with step number k=7 and thereby making them suitable for the solution of stiff ordinary differential equations. The new methods proposed in this paper turn out to be A-stable. Numerical examples obtained demonstrate the accuracy and efficiency of the new Blended Block Linear Multistep Methods.
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