Abstract
General linear multistep methods which include those of Holyhead et al. [9] and Gladwin et al. [8] are introduced. A new simple root condition for stability is deduced. A theorem relating the coefficients of this new associated stability polynomial to those of the method is proved. This permits a constructive approach for obtaining high accuracy convergent methods. Two such methods are derived and numerical results are presented.
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This work was done under the financial support of: Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), and Financiadora Nacional de Empreendimentos e Projetos (FINEP)—Ministério do Planejamento (Brazil).
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Andrade, C., McKee, S. On optimal high accuracy linear multistep methods for first kind volterra integral equations. BIT 19, 1–11 (1979). https://doi.org/10.1007/BF01931215
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DOI: https://doi.org/10.1007/BF01931215