Blended block BVMs (B\(_3\)VMs): A family of economical implicit methods for ODEs
The so called blended linear multistep methods were introduced by \textit{R. D. Skeel} and \textit{A. K. Kong} [ACM Trans. Math. Softw. 3, 326-345 (1977; Zbl 0399.65045)] as a means to circumvent the stability barriers of standard linear multistep formulas for the numerical solution of stiff initial value problems. In the paper under consideration this idea is translated to the so called boundary value methods in order to derive methods with a cheap implementation as well as good stability properties. The paper is organized as follows: In section 2 the relevant properties of block boundary value methods are briefly reviewed. Section 3 introduces the blended methods and studies some families of them. Finally, in the last section, some numerical experiments are presented to compare the behaviour of the new methods with the block boundary value methods used in the generalized Adams methods of \textit{F. Iavernaro} and \textit{F. Mazzia} [Appl. Numer. Math. 28, No. 2-4, 107-126 (1998; Zbl 0926.65076)].
scientific article; zbMATH DE number 1437652