A Fast Convergent Approximation Method for the Solution of Second Order Linear Ordinary Differential Equations

Authors

  • Gevorg A. Grigorian Institute of Mathematics NAS of Armenia 0019 Armenia c. Yerevan, str. M. Bagramian 24/5

DOI:

https://doi.org/10.5644/SJM.19.02.09

Keywords:

Riccati equation, Peano's existence theorem, second order linear ordinary differential equations, fundamental matrices of level $m$, gluing of fundamental matrices

Abstract

The Riccati equation method is used to obtain a fast convergent approximation method for the solution of second order linear ordinary differential equations. By using examples it is shown how fast the proposed method can converge.

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References

A. A. Anulo, A. Sh. Kibrit, G. G. Gonfa, A. D. Negasa, Numerical Solution of Linear Second Order Ordinary Differential Equations with Mixed Boundary Conditions by Galerkin Method, Mathematics and Computer Science, vol. 2, issue 5, 2017, pp. 66-78.

F. W. J. Olver, Numerical Solution of Second-Order Linear Difference Equations. Journal of Research of the National Bureou of Standards - B, Mathematics and Mathematical Physics, vol. 71 B, Nos. 2 and 3, 1967, pp. 111-129.

Y. A. Yahaya and A. M. Badmus, A class of collocation methods for general second order ordinary differential equations, African Journal of Mathematics and Computer Sciences Research, vol 2 (4) 2009, pp. 069-072.

T. Chen, W. Chen, G. Chen, H. He, Recursive formulation of WKB solution for linear time-varying dynamic systems, Acta Mech., vol 232, 2021, pp. 907-920.

O. A. Taivo and J. A. Osilagun, On Approximate Solution of Second Order Differential Equations by Iterative decomposition Method, Asian Journal of Mathematics and Statistics, 4 (1), 2011, pp. 1--7.

Md. J. Hossein, Md. Sh. Alam, Md. B. Hossein, A Study on Numerical Solution of Second Order Initial Value Problem (IVP) for Ordinary Differential Equations with Four order and Butcher's Fifth Order Runge Kutta Method, American Journal of Computational and Applied Mathematics, 7 (5), 2017, pp 129--137.

N. Waeleh & Z. A. Majid, Numerical Algorithm of Block Method for General Second Order ODEs using Variable Step Size, Sains Malaysiana, 46 (5), 2017, pp. 817--824.

N. Echi, Approximate Solution of Second-Order Linear Differential Equation, Open Access Scientific Reports, vol. 2, issue 1, 2013, pp. 1--5.

J. E. Mamadu, I. N. Njoseh, Tau-Collocation Approximation Approach for Solving First and Second Order Ordinary Differential Equations, Journal of Applied Mathematics and Physics, 4, 2016, pp. 384--390.

T. G. Nezbajlo, Theory of integration of linear ordinary differential equations, Sanct Peterburg, 2007, 160 pages.

Ph. Hartman, Ordinary differential Equations. Second Edition, SIAM, 2002.

N. W. McLachlan, Theory and Application of Mathieu Functions. Oxford: Claredon Press, 1947.

L. Chezari, Asimptoticheskoe povedenie i ustoichivost reshenii obyknovennykh differentsialnykh uravnenii, Mir, M., 1964.

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Published

25.01.2024

How to Cite

Grigorian, G. A. (2024). A Fast Convergent Approximation Method for the Solution of Second Order Linear Ordinary Differential Equations. Sarajevo Journal of Mathematics, 19(2), 241–253. https://doi.org/10.5644/SJM.19.02.09

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