Abstract
A two-parameter family of algorithms for finding an approximate solution to a linear two-point boundary value problem for a system of ordinary differential equations is offered. The convergence conditions for the algorithms are obtained. The necessary and sufficient coefficient conditions for the well-posedness of considered problem are established.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
A. A. Abramov, ‘‘On the transfer of boundary conditions for systems of ordinary linear differential equations (a variant of the dispersive method),’’ USSR Comput. Math. Math. Phys. 1, 617–622 (1962).
R. P. Agarwal, Boundary Value Problems for Higher Order Differential Equations (World Scientific, Singapore, Philadelphia, 1986).
R. P. Agarwal and R. C. Gupta, Essentials of Ordinary Differential Equations (McGraw-Hill, Singapore, New York, 1991).
R. P. Agarwal, Focal Boundary Value Problems for Differential and Difference Equations (Kluwer Academic, Dordrecht, 1998).
R. P. Agarwal, S. R. Grace, and D. O’Regan, Oscillation Theory for Second Order Linear (Kluwer Academic, The Netherlands, 2002).
R. P. Agarwal and V. Lakshmikantham, Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations (World Scientific, Singapore, 1993).
R. P. Agarwal and D. O’Regan, An Introduction to Ordinary Differential Equations (Springer Science, New York, 2008).
D. S. Dzhumabayev, ‘‘Criteria for the unique solvability of a linear boundary-value problem for an ordinary differential equation,’’ USSR Comput. Math. Math. Phys. 29, 34–46 (1989).
H. Keller, Numerical Methods for Two-Point Boundary Value Problems (Walthan, Blaisdell, 1968).
I. T. Kiguradze, ‘‘Boundary value problems for systems of ordinary differential equations,’’ Itogi Nauki Tekh., Ser.: Sovrem. Probl. Mat. Nov. Dostizh. 30, 3–103 (1987).
S. M. Roberts and J. S. Shipman, Two-Point Boundary-Value Problems: Shooting Methods (Elsevier, New York, 1972).
M. Ronto and A. M. Samoilenko, Numerical-Analytic Methods for Investigation of Periodic Solutions (World Scientific, Singapore etc., 2000).
S. K. Sen and R. P. Agarwal, p, e, f with MATLAB: Random and Rational Sequences with Scope in Supercomputing Era (Cambridge Scientific, Cambridge, 2011).
T. K. Yuldashev and J. A. Artykova, ‘‘Volterra functional integral equation of the first kind with nonlinear right-hand side and variable limits of integration,’’ Ukr. Math. J. 58, 1458–1461 (2006).
Funding
This research has was funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (grant no. AP08956612).
Author information
Authors and Affiliations
Corresponding authors
Additional information
(Submitted by T. K. Yuldashev)
Rights and permissions
About this article
Cite this article
Temesheva, S.M., Dzhumabaev, D.S. & Kabdrakhova, S.S. On One Algorithm To Find a Solution to a Linear Two-Point Boundary Value Problem. Lobachevskii J Math 42, 606–612 (2021). https://doi.org/10.1134/S1995080221030173
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080221030173