Approximate solution of the special type differential equation of higher order using Taylor's series

Volume 27, Issue 2, pp 131--141 http://dx.doi.org/10.22436/jmcs.027.02.04

Publication Date: April 13, 2022 Submission Date: December 19, 2021 Revision Date: January 17, 2022 Accteptance Date: February 01, 2022

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 789 Downloads
• 2143 Views

Authors

A. P. Selvan - Department of Mathematics, Kings Engineering College, Irungattukottai, Sriperumbudur, Chennai, 602 117, Tamil Nadu, India. S. Sabarinathan - Department of Mathematics, SRM Institute of Science \(\&\) Technology, Kattankulthur, 603 203, Tamil Nadu, India. A. Selvam - Department of Mathematics, SRM Institute of Science \(\&\) Technology, Kattankulthur, 603 203, Tamil Nadu, India.

Abstract

We study the approximate solution of the special type \(n^{th}\) order linear differential equation by applying initial and boundary conditions using Taylor's series formula. That is, we prove the sufficient condition for the Mittag-Leffler-Hyers-Ulam stability and Mittag-Leffler-Hyers-Ulam-Rassias stability of the special type linear differential equation of higher order with initial and boundary conditions using Taylor's series formula.

Share and Cite

Keywords

• Mittag-Leffler-Hyers-Ulam stability
• Mittage-Leffler-Hyers-Ulam-Rassias stability
• linear differential equations
• initial and boundary conditions
• Taylor's series formula

MSC

•  34K20
•  26D10
•  44A10
•  39B82
•  34A40
•  39A30

References

• [1] M. R. Abdollahpour, R. Aghayari, M. T. Rassias, Hyers-Ulam stability of associated Laguerre differential equations in a subclass of analytic functions, J. Math. Anal. Appl., 437 (2016), 605--612
  • View Article
  • MathSciNet


• [2] M. Almahalebi, A. Chahbi, S. Kabbaj, A fixed point approach to the stability of a bi-cubic functional equations in 2-Banach spaces, Palest. J. Math., 5 (2016), 220--227
  • View Article
  • MathSciNet


• [3] Q. H. Alqifiary, S. M. Jung, Hyers-Ulam stability of second-order linear differential equations with boundary conditions, SYLWAN, 158 (2014), 289--301
  • View Article
  • Google Scholar


• [4] C. Alsina, R. Ger, On some inequalities and stability results related to the exponential function, J. Inequal. Appl., 2 (1998), 373--380
  • View Article
  • MathSciNet
  • MATH


• [5] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64--66
  • View Article
  • MathSciNet
  • MATH


• [6] D. G. Bourgin, Classes of transformations and bordering transformations, Bull. Amer. Math. Soc., 57 (1951), 223--237
  • View Article
  • MathSciNet


• [7] N. Brillouët-Belluot, J. Brzdȩk, K. Ciepliński, On some recent developments in Ulam's type stability, Abstr. Appl. Anal., 2012 (2012), 41 pages
  • View Article
  • MathSciNet
  • MATH


• [8] M. Burger, N. Ozawa, A. Thom,, On Ulam stability, Israel J. Math., 193 (2013), 109--129
  • View Article
  • MathSciNet


• [9] L. Cadariu, L. Gavruta, P. Gavruta, Fixed points and generalized Hyers-Ulam stability, Abstr. Appl. Anal., 2012 (2012), 10 pages
  • View Article
  • MathSciNet


• [10] G. Choi, S.-M. Jung, Invariance of Hyers-Ulam stability of linear differential equations and its applications, Adv. Difference Equ., 2015 (2015), 14 pages
  • View Article
  • MathSciNet


• [11] P. Gavruta, S.-M. Jung, Y. G. Li, Hyers-Ulam stability for second order linear differential equations with boundary conditions, Electron. J. Differential Equations, 2011 (2011), 5 pages
  • View Article
  • MathSciNet


• [12] J. Huang, Q. H. Alqifiary, Y. Li, On the generalized superstability of $n$th-order linear differential equations with initial conditions, Publications De L'Institut Mathematique, Nouvelle serie, 98 (2015), 243--249
  • View Article
  • Google Scholar


• [13] J. H. Huang, S. M. Jung, Y. J. Li, On Hyers-Ulam stability of Non-linear differential equations, Bull. Korean Math. Soc., 52 (2015), 685--697
  • View Article
  • Google Scholar


• [14] J. H. Huang, Y. J. Li, Hyers-Ulam stability of linear differential equations, J. Math. Anal. Appl., 426 (2015), 1192--1200
  • View Article
  • MathSciNet


• [15] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 27 (1941), 222--224
  • View Article
  • MathSciNet


• [16] S.-M. Jung, Hyers-Ulam-Rassias stability of functional equation in nonlinear analysis, Springer, New York (2011)
  • View Article
  • MathSciNet


• [17] S.-M. Jung, J. Roh, J. Lee, Optimal Hyers-Ulam's constant for the linear differential equations, J. Inequal. Appl., 2016 (2016), 7 pages
  • View Article
  • MathSciNet


• [18] T. X. Li, A. Zada, S. Faisal, Hyers--Ulam stability of nth order linear differential equations, J. Nonlinear Sci. Appl., 9 (2016), 2070--2075
  • View Article
  • Google Scholar


• [19] R. Murali, A. Bodaghi, A. Ponmana Selvan, Stability for the third order linear ordinary differential equation, Int. J. Math. Comput., 30 (2019), 87--92
  • Google Scholar


• [20] R. Murali, A. Ponmana Selvan, On the generalized Hyers-Ulam stability of linear ordinary differential equations of higher order, Int. J. Pure Appl. Math., 117 (2017), 317--326
  • View Article
  • Google Scholar


• [21] R. Murali, A. Ponmana Selvan, Hyers-Ulam stability of $n$th order differential equation, Contemp. Stud. Discrete Math., 2 (2018), 45--50
  • Google Scholar


• [22] R. Murali, A. Ponmana Selvan, Hyers-Ulam-Rassias stability for the linear ordinary differential equation of third order, Kragujevac J. Math., 42 (2018), 579--590
  • View Article
  • MathSciNet


• [23] R. Murali, A. Ponmana Selvan, Ulam stability of a LCR electric circuit with electromotive force, Int. J. Math. Appl., 6 (2018), 62--66
  • View Article
  • Google Scholar


• [24] R. Murali, A. Ponmana Selvan, Hyers-Ulam stability of $n$th order linear differential equation, Kragujevac J. Math., 38 (2019), 553--566
  • View Article
  • Google Scholar


• [25] R. Murali, A. Ponmana Selvan, C. Park, Ulam stability of linear differential equations using Fourier transform, AIMS Math., 5 (2019), 766--780
  • View Article
  • MathSciNet


• [26] R. Murali, A. Ponmana Selvan, Hyers--Ulam stability of a free and forced vibrations, Kragujevac J. Math., 44 (2020), 299--312
  • View Article
  • MathSciNet


• [27] R. Murali, M. J. Rassias, V. Vithya, The general solution and stability of nonadecic functional equation in matrix normed spaces, Malaya J. Mat., 5 (2017), 416--427
  • View Article
  • Google Scholar


• [28] M. Obloza, Hyers stability of the linear differential equation, Rocznik Nauk.-Dydakt. Prace Mat., 13 (1993), 259--270
  • MathSciNet
  • Google Scholar
  • MATH


• [29] M. Obloza, Connections between Hyers and Lyapunov stability of the ordinary differential equations, Rocznik Nauk.-Dydakt. Prace Mat., 14 (1997), 141--146
  • MathSciNet
  • Google Scholar
  • MATH


• [30] M. Onitsuka, T. Shoji, Hyers-Ulam stability of first order homogeneous linear differential equations with a real-valued co-efficient, Appl. Math. Lett., 63 (2017), 102--108
  • View Article
  • Google Scholar


• [31] T. M. Rassias, On the stability of linear mappings in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297--300
  • View Article
  • MathSciNet


• [32] K. Ravi, R. Murali, A. Ponmana Selvan, Hyers--Ulam stability of $n$th order linear differential equation with initial and boundary condition, Asian J. Math. Comput. Res., 11 (2016), 201--207
  • View Article
  • Google Scholar


• [33] K. Ravi, R. Murali, A. Ponmana Selvan, Ulam stability of a general $n$th order linear differential equation with constant coefficients, Asian J. Math. Comput. Res., 11 (2016), 61--68
  • View Article
  • Google Scholar


• [34] K. Ravi, J. M. Rassias, S. Pinelas, S. Suresh, General solution and stability of Quattuordecic functional equation in quasi-$beta$-normed spaces, Adv. pure Math., 6 (2016), 921--941
  • View Article
  • Google Scholar


• [35] K. Ravi, J. M. Rassias, B. V. Senthil Kumar, Ulam-Hyers stability of undecic functional equation in quasi-$beta$-normed spaces fixed point method, Tbilisi Math. Sci., 9 (2016), 83--103
  • View Article
  • Google Scholar


• [36] S. Takahasi, T. Miura, S. Miyajima, On the Hyers-Ulam stability of the Banach space valued differential equation $y^{'} (t) = \lambda \ y(t)$, Bull. Korean Math. Soc., 39 (2002), 309--315
  • View Article
  • Google Scholar


• [37] S. M. Ulam, A Collection of Mathematical Problems, Interscience Publisheres, New York-London (1960)
  • View Article
  • Google Scholar