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Abstract

Psychology and Psychotherapy: Research Study

Laws of Dahlquist in Multistep Methods and Some of their Modification

  • Open or CloseImanova Mehriban1,3 and Vagif Ibrahimov2,3*

    1Science Development Foundation under the President of the Republic of Azerbaijan, Baku, Azerbaijan

    2Chief of the Department of Computational Mathematics, Baku State University, Baku, Azerbaijan

    3Institute of Control Systems, Azerbaijan National Academy of Sciences, Baku, Azerbaijan

    *Corresponding author:Vagif Ibrahimov, Chief of the Department of Computational Mathematics, Baku State University, Institute of Control Systems, Azerbaijan National Academy of Sciences, Baku, Azerbaijan

Submission: October 25, 2024;Published: November 08, 2024

DOI: 10.31031/SIAM.2024.05.000607

ISSN 2639-0612
Volume5 Issue2

Abstract

No one doubts the relevance Multistep Methods with constant coefficients and their applications to solve different problems of Natural science. The base search for these methods was carried out by the Dahlquist. Based on this, here the description of some development of these theories and the application to solve Ordinary Differentia the Volterra Integral and the Volterra Integro-Differential Equations. Here, investigated advanced (forward-jumping) methods, and comprised the results receiving for the advanced method with the Dahlquist results. Here, have investigated the second derivative multistep methods of advanced type and shown that stable methods of advanced methods are more exact. In addition, fined the maximum value for the degree of the advanced method. Constructed methods the illustrated receiving results.

Keywords:Initial-value problem; Ordinary differential equation; The volterra integro-differential equation; Stability and degree; Multistep multiderivative methods

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