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DISCRETE METHOD FOR SOLVING A THREE-POINT BOUNDARY-VALUE PROBLEM FOR A THIRD-ORDER EQUATION

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Abstract

Adjoined equations are used to develop a method for solving boundary-value problems for second- and third-order equations. With the use of the factorization method, a three-point boundary-value problem for a third-order equation is reduced to a system of first- and second-order equations. In order to solve the second-order equation, a discrete problem is constructed, which is then used to solve the main problem. This method is peculiar because discrete (difference) boundary-value problems are constructed without using approximations of differential operators. The method is generalized to solve higher-order equations.

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Authors and Affiliations

  1. Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    A. F. Voevodin & O. A. Frolovskaya

Authors
  1. A. F. Voevodin
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  2. O. A. Frolovskaya
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Correspondence to O. A. Frolovskaya.

Additional information

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Vol. 62, No. 6, pp. 20-26. https://doi.org/10.15372/PMTF20210603.

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Voevodin, A.F., Frolovskaya, O.A. DISCRETE METHOD FOR SOLVING A THREE-POINT BOUNDARY-VALUE PROBLEM FOR A THIRD-ORDER EQUATION. J Appl Mech Tech Phy 62, 906–911 (2021). https://doi.org/10.1134/S0021894421060031

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  • DOI: https://doi.org/10.1134/S0021894421060031

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