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

A. Asanov; E. Hazar; M. Abdujabbarov

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

Year 2016, Volume: 4 Issue: 2, 42 - 51, 01.10.2016

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] Delves L.M., Walsh J., (1974) Numerical Solution of Integral Equations, Clarendon, Oxford England
[2] Wolfgang H. (1995), Integral Equations theory and numerical treatment, Birkhauser, Basel Germany
[3] Atkinson K., Han W., (2009) Theoretical and Numerical Analysis, Springer, New York USA
[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] 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] 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] Asanov A., (1998) Regularization, Uniqueness and Existence of Solutions of Volterra Equations of the First Kind, VSP, Utrecht, The Netherlands, 272
[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] Asanov A., (2002) Volterra – Stieltjes Integral Equations of the Second and First Kind Manas Journal of Engineering, No 2, 79-95

İkinci Tip Lineer Volterra-Stieltjes İntegral Denkleminin Genelleşmiş Orta Nokta Kuralı ile Cözümü

Year 2016, Volume: 4 Issue: 2, 42 - 51, 01.10.2016

A. Asanov E. Hazar M. Abdujabbarov

Abstract

Bu çalışmada İkinci türden lineer Volterra –Stieljes integral denklemi için orta nokta kuralı kullanılarak, sayısal çözüm kurulmuş ve incelenmiştir. Ayrıca hata tahmini ile ilgili koşullar belirlenmiş ve ispat edilmiştir. Önerilen yöntemle bir örnek çözülmüştür

Keywords

lineer Volterra –Stieljes integral denklemi, İkinci türden lineer integral denklemi, geneleştirilmiş orta nokta kuralı, hata tahmini

References

[1] Delves L.M., Walsh J., (1974) Numerical Solution of Integral Equations, Clarendon, Oxford England
[2] Wolfgang H. (1995), Integral Equations theory and numerical treatment, Birkhauser, Basel Germany
[3] Atkinson K., Han W., (2009) Theoretical and Numerical Analysis, Springer, New York USA
[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] 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] 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] Asanov A., (1998) Regularization, Uniqueness and Existence of Solutions of Volterra Equations of the First Kind, VSP, Utrecht, The Netherlands, 272
[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] Asanov A., (2002) Volterra – Stieltjes Integral Equations of the Second and First Kind Manas Journal of Engineering, No 2, 79-95

There are 9 citations in total.

Details

Other ID	JA78ZU99ER
Journal Section	Research Article
Authors	A. Asanov This is me E. Hazar This is me M. Abdujabbarov This is me
Publication Date	October 1, 2016
Published in Issue	Year 2016 Volume: 4 Issue: 2

Cite

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.
AMA	Asanov A, Hazar E, Abdujabbarov M. Solution Of Linear Volterra – Stieltjes Integral Equation Of The Second Kind Using Generalized Midpoint Rule. MJEN. October 2016;4(2):42-51.
Chicago	Asanov, A., E. Hazar, and M. Abdujabbarov. “Solution Of Linear Volterra – Stieltjes Integral Equation Of The Second Kind Using Generalized Midpoint Rule”. MANAS Journal of Engineering 4, no. 2 (October 2016): 42-51.
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	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, 2016.
ISNAD	Asanov, A. et al. “Solution Of Linear Volterra – Stieltjes Integral Equation Of The Second Kind Using Generalized Midpoint Rule”. MANAS Journal of Engineering 4/2 (October 2016), 42-51.
JAMA	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, 2016, pp. 42-51.
Vancouver	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.