Solution Of Linear Volterra – Stieltjes Integral Equation Of The Second Kind Using Generalized Midpoint Rule

Volume: 4 Number: 2 October 1, 2016
A. Asanov , E. Hazar , M. Abdujabbarov
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Solution Of Linear Volterra – Stieltjes Integral Equation Of The Second Kind Using Generalized Midpoint Rule

Abstract

In this study, the numerical solution of linear Volterra – Stieltjes equations of the second kind by using the generalized midpoint rule is established and investigated. The conditions on estimation of the error are determined and proved. One example is solved employing the proposed method.

Keywords

Volterra – Stieltjes integral equation, linear integral equation of the second kind, generalized midpoint rule, error estimation.

References

  1. [1] Delves L.M., Walsh J., (1974) Numerical Solution of Integral Equations, Clarendon, Oxford England
  2. [2] Wolfgang H. (1995), Integral Equations theory and numerical treatment, Birkhauser, Basel Germany
  3. [3] Atkinson K., Han W., (2009) Theoretical and Numerical Analysis, Springer, New York USA
  4. [4] Majeed S.M., (2014) Modified Midpoint Method for Solving System of Linear Fredholm Integral Equations of the Second Kind, American Journal of Applied Mathematics, Volume 2. No 5, 155-161
  5. [5] Asanov A. , Chelik M.H., Abdujabbarov M. (2011) Approximating the Stieltjes Integral Using the Generalized Midpoint Rule, Matematika, Volume 27, Number 2, 139-148
  6. [6] Asanov A., Abdujabbarov M. (2015) Solving Linear Fredholm-Stieltjes Integral Equations of the Second Kind by Using the Generalized Midpoint Rule, Journal of Mathematics and System Science, Volume 5, 459-463
  7. [7] Asanov A., (1998) Regularization, Uniqueness and Existence of Solutions of Volterra Equations of the First Kind, VSP, Utrecht, The Netherlands, 272
  8. [8] Asanov A., (2001) The derivative of a function by means of an increasing function, Manas Journal of Engineering, No 1, 18-67 (in Russian)
  9. [9] Asanov A., (2002) Volterra – Stieltjes Integral Equations of the Second and First Kind Manas Journal of Engineering, No 2, 79-95

Details

Primary Language

English

Subjects

-

Journal Section

-

Authors

A. Asanov This is me

E. Hazar This is me

M. Abdujabbarov This is me

Publication Date

October 1, 2016

Submission Date

October 1, 2016

Acceptance Date

-

Published in Issue

Year 2016 Volume: 4 Number: 2

IZ

https://izlik.org/JA34NA39WW

Cite

RIS / Bibtex
APA
Asanov, A., Hazar, E., & Abdujabbarov, M. (2016). Solution Of Linear Volterra – Stieltjes Integral Equation Of The Second Kind Using Generalized Midpoint Rule. MANAS Journal of Engineering, 4(2), 42-51. https://izlik.org/JA34NA39WW
AMA
1.Asanov A, Hazar E, Abdujabbarov M. Solution Of Linear Volterra – Stieltjes Integral Equation Of The Second Kind Using Generalized Midpoint Rule. MJEN. 2016;4(2):42-51. https://izlik.org/JA34NA39WW
Chicago
Asanov, A., E. Hazar, and M. Abdujabbarov. 2016. “Solution Of Linear Volterra – Stieltjes Integral Equation Of The Second Kind Using Generalized Midpoint Rule”. MANAS Journal of Engineering 4 (2): 42-51. https://izlik.org/JA34NA39WW.
EndNote
Asanov A, Hazar E, Abdujabbarov M (October 1, 2016) Solution Of Linear Volterra – Stieltjes Integral Equation Of The Second Kind Using Generalized Midpoint Rule. MANAS Journal of Engineering 4 2 42–51.
IEEE
[1]A. Asanov, E. Hazar, and M. Abdujabbarov, “Solution Of Linear Volterra – Stieltjes Integral Equation Of The Second Kind Using Generalized Midpoint Rule”, MJEN, vol. 4, no. 2, pp. 42–51, Oct. 2016, [Online]. Available: https://izlik.org/JA34NA39WW
ISNAD
Asanov, A. - Hazar, E. - Abdujabbarov, M. “Solution Of Linear Volterra – Stieltjes Integral Equation Of The Second Kind Using Generalized Midpoint Rule”. MANAS Journal of Engineering 4/2 (October 1, 2016): 42-51. https://izlik.org/JA34NA39WW.
JAMA
1.Asanov A, Hazar E, Abdujabbarov M. Solution Of Linear Volterra – Stieltjes Integral Equation Of The Second Kind Using Generalized Midpoint Rule. MJEN. 2016;4:42–51.
MLA
Asanov, A., et al. “Solution Of Linear Volterra – Stieltjes Integral Equation Of The Second Kind Using Generalized Midpoint Rule”. MANAS Journal of Engineering, vol. 4, no. 2, Oct. 2016, pp. 42-51, https://izlik.org/JA34NA39WW.
Vancouver
1.A. Asanov, E. Hazar, M. Abdujabbarov. Solution Of Linear Volterra – Stieltjes Integral Equation Of The Second Kind Using Generalized Midpoint Rule. MJEN [Internet]. 2016 Oct. 1;4(2):42-51. Available from: https://izlik.org/JA34NA39WW

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