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Stability and Convergence of Multistep Methods for Linear Volterra Integral Equations of the First Kind

1976; Society for Industrial and Applied Mathematics; Volume: 13; Issue: 2 Linguagem: Inglês

10.1137/0713026

1095-7170

P. A. W. Holyhead, S. McKee,

Fractional Differential Equations Solutions

This paper is concerned with deriving necessary and sufficient conditions for multistep methods to be convergent. The conditions require that the zeros of an analytic function defined by a determinant of analytic functions all lie outside the unit circle. It is demonstrated that this condition is equivalent to the eigenvalue condition obtained in a previous paper (Holyhead, McKee and Taylor (1975)). The concepts of strong and weak stability are also introduced. A weakly stable method is given.