Blended Linear Multistep Methods

The accuracy of linear multistep formulas suitable for stiff differential systems is limited. Greater accuracy can be attained by including higher derivatives in the formula, but this is not practical for all problems. However, it is possible to duplicate the absolute stability region for any given m-derivative multistep formula by taking a combination of m multistep formulas. These blended formulas are similar to Lambert and Sigurdsson's linear multistep formulas with variable matrix coefficients, but the approach is different. Implementation details and numerical results are presented for a variable-order, variable-step blend of the Adams-Moulton and the backward differentiation formulas.