Numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument

• Autorzy: Abregov M. H. , Kanchukoev V. Z. , Shardanova M. A.

Identyfikatory

DOI

10.1515/jaa-2017-0018

• Języki publikacji: EN

Abstrakty

EN

This work is devoted to the numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument in minor terms. The sufficient conditions of the one-valued solvability are established, and the a priori estimate of the solution is obtained. For the numerical solution, the problem studied is reduced to the equivalent boundary value problem for an ordinary linear differential equation of fourth order, for which the finite-difference scheme of second-order approximation was built. The convergence of this scheme to the exact solution is shown under certain conditions of the solvability of the initial problem. To solve the finite-difference problem, the method of five-point marching of schemes is used.

Słowa kluczowe

EN

equation with deviating argument; a priori estimate of solution; finite difference scheme; method of marching for five-point systems

PL

równanie z odchylonymi argumentami; szacowanie a priori; schemat różnic skończonych

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2017
• Tom: Vol. 23, nr 2
• Strony: 141--146
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Abregov M. H.

• Department of Physical and Mathematical Sciences, Kabardino-Balkarian State University, Chernyshevskogo Str. 173, Nalchik 360004, Russia

autor

Kanchukoev V. Z.

• Department of Physical and Mathematical Sciences, Kabardino-Balkarian State University, Chernyshevskogo Str. 173, Nalchik 360004, Russia

autor

Shardanova M. A.

• Department of Differential Equations, Kabardino-Balkarian State University, Chernyshevskogo Str. 173, Nalchik 360004, Russia

Bibliografia

• [1] M. H. Abregov, V. Z. Kanchukoev and M. A. Shardanova, Numerical methods for solving the first kind boundary value problem for a linear second order differential equation with a deviating argument on a symmetric interval, Int. Research J. (2016), no. 5(47), 11-15.
• [2] M. H. Abregov, V. Z. Kanchukoev and M. A. Shardanova, The first kind boundary value problem for a linear second order differential equation with a deviating argument on a symmetric interval, Int. Research J. (2016), no. 5(47), 6-11.
• [3] A. B. Mudrov, On the relations of the systems of ordinary differential equations and equations with a delayed agrument, Bull. Novosibirsk State Univ. 7 (2007), no. 2, 52-64.
• [4] S. B. Norkin, Differential Equations of the Second Order with Retarded Argument, Transl. Math. Monogr. 31, American Mathematical Society, Providence, 1965.
• [5] A. V. Prosolov, Dynamic Models with Delay and Their Applications in Economics and Engineering, LAN Publishing, St. Peterburg, 2010.
• [6] A. A. Samarskiy, The Theory of Difference Schemes, The Science, Moscow, 1989.
• [7] N. A. Tikhonov, A. B. Vasil’eva and A. G. Sveshnikov, Differential Equations, Fizmatlit, Moscow, 1985.
• [8] A. B. Vasil’eva and N. A. Tikhonov, Integral Equations, Fizmatlit, Moscow, 2002.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).