A GALERKIN-TYPE METHOD FOR SOLUTIONS OF PANTOGRAPH-TYPE VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS WITH FUNCTIONAL UPPER LIMIT

Şuayip Yüzbaşı; Murat Karaçayır

A GALERKIN-TYPE METHOD FOR SOLUTIONS OF PANTOGRAPH-TYPE VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS WITH FUNCTIONAL UPPER LIMIT

Abstract

In this study, we present a Galerkin-type method for obtaining approximate solutions of linear Volterra-Fredholm delay integro-differential equations with a functional upper limit under mixed conditions. The method gives an approximate solution of the problem in power series form truncated after a certain term. Using an integer value N as the truncation point and making use of the matrix representations of a polynomial and its derivatives, we obtain the matrix form of the problem expressed in terms of the approximate solution polynomial. By applying inner product to these relations with monomials up to degree N and incorporating the mixed conditions, the problem is reduced to a system of linear algebraic equations. The approximate solution of the problem is then determined from this linear system. In addition, we discuss a way of improving an obtained approximate solution by means of its estimated error function. The presented scheme has the advantages of (1) being applicable to a wide range of problems including pantograph-type equations with or without Fredholm and Volterra integral terms, and (2) giving accurate results as demonstrated by applications to example problems taken from existing studies.

Keywords

References

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Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Şuayip Yüzbaşı This is me
0000-0002-5838-7063
Türkiye

Murat Karaçayır This is me
0000-0001-6230-3638
Türkiye

Publication Date

June 1, 2021

Submission Date

January 27, 2020

Acceptance Date

April 2, 2020

Published in Issue

Year 2020 Volume: 38 Number: 2

IZ

https://izlik.org/JA72ZA47SB

Cite

RIS / Bibtex

APA

Yüzbaşı, Ş., & Karaçayır, M. (2021). A GALERKIN-TYPE METHOD FOR SOLUTIONS OF PANTOGRAPH-TYPE VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS WITH FUNCTIONAL UPPER LIMIT. Sigma Journal of Engineering and Natural Sciences, 38(2), 995-1005. https://izlik.org/JA72ZA47SB

AMA

1.Yüzbaşı Ş, Karaçayır M. A GALERKIN-TYPE METHOD FOR SOLUTIONS OF PANTOGRAPH-TYPE VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS WITH FUNCTIONAL UPPER LIMIT. SIGMA. 2021;38(2):995-1005. https://izlik.org/JA72ZA47SB

Chicago

Yüzbaşı, Şuayip, and Murat Karaçayır. 2021. “A GALERKIN-TYPE METHOD FOR SOLUTIONS OF PANTOGRAPH-TYPE VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS WITH FUNCTIONAL UPPER LIMIT”. Sigma Journal of Engineering and Natural Sciences 38 (2): 995-1005. https://izlik.org/JA72ZA47SB.

EndNote

Yüzbaşı Ş, Karaçayır M (June 1, 2021) A GALERKIN-TYPE METHOD FOR SOLUTIONS OF PANTOGRAPH-TYPE VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS WITH FUNCTIONAL UPPER LIMIT. Sigma Journal of Engineering and Natural Sciences 38 2 995–1005.

IEEE

[1]Ş. Yüzbaşı and M. Karaçayır, “A GALERKIN-TYPE METHOD FOR SOLUTIONS OF PANTOGRAPH-TYPE VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS WITH FUNCTIONAL UPPER LIMIT”, SIGMA, vol. 38, no. 2, pp. 995–1005, June 2021, [Online]. Available: https://izlik.org/JA72ZA47SB

ISNAD

Yüzbaşı, Şuayip - Karaçayır, Murat. “A GALERKIN-TYPE METHOD FOR SOLUTIONS OF PANTOGRAPH-TYPE VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS WITH FUNCTIONAL UPPER LIMIT”. Sigma Journal of Engineering and Natural Sciences 38/2 (June 1, 2021): 995-1005. https://izlik.org/JA72ZA47SB.

JAMA

1.Yüzbaşı Ş, Karaçayır M. A GALERKIN-TYPE METHOD FOR SOLUTIONS OF PANTOGRAPH-TYPE VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS WITH FUNCTIONAL UPPER LIMIT. SIGMA. 2021;38:995–1005.

MLA

Yüzbaşı, Şuayip, and Murat Karaçayır. “A GALERKIN-TYPE METHOD FOR SOLUTIONS OF PANTOGRAPH-TYPE VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS WITH FUNCTIONAL UPPER LIMIT”. Sigma Journal of Engineering and Natural Sciences, vol. 38, no. 2, June 2021, pp. 995-1005, https://izlik.org/JA72ZA47SB.

Vancouver

1.Şuayip Yüzbaşı, Murat Karaçayır. A GALERKIN-TYPE METHOD FOR SOLUTIONS OF PANTOGRAPH-TYPE VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS WITH FUNCTIONAL UPPER LIMIT. SIGMA [Internet]. 2021 Jun. 1;38(2):995-1005. Available from: https://izlik.org/JA72ZA47SB