Yıl 2018, Cilt 22, Sayı 6, Sayfalar 1659 - 1668 2018-12-01
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## A numerical technique based on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points for solving functional integro-differential equations involving variable delays

#### Sevin Gümgüm [1] , Nurcan Baykuş Savaşaneril [2] , Ömür Kıvanç Kürkçü [3] , Mehmet Sezer [4]

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In this paper, a new numerical matrix-collocation technique is considered to solve functional integro-differential equations involving variable delays under the initial conditions. This technique is based essentially on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points. Some descriptive examples are performed to observe the practicability of the technique and the residual error analysis is employed to improve the obtained solutions. Also, the numerical results obtained by using these collocation points are compared in tables and figures.

Functional equations, Matrix technique, Lucas polynomials, Residual error analysis.
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Birincil Dil en Matematik December 2018 Araştırma Makalesi Orcid: 0000-0002-0594-2377Yazar: Sevin Gümgüm (Sorumlu Yazar)Kurum: İZMİR EKONOMİ ÜNİVERSİTESİÜlke: Turkey Orcid: 0000-0002-3098-2936Yazar: Nurcan Baykuş SavaşanerilKurum: DOKUZ EYLÜL ÜNİVERSİTESİÜlke: Turkey Orcid: 0000-0002-3987-7171Yazar: Ömür Kıvanç KürkçüKurum: İZMİR EKONOMİ ÜNİVERSİTESİÜlke: Turkey Orcid: 0000-0002-7744-2574Yazar: Mehmet SezerKurum: CELÂL BAYAR ÜNİVERSİTESİÜlke: Turkey
 Bibtex @araştırma makalesi { saufenbilder384592, journal = {Sakarya University Journal of Science}, issn = {1301-4048}, eissn = {2147-835X}, address = {Sakarya Üniversitesi}, year = {2018}, volume = {22}, pages = {1659 - 1668}, doi = {10.16984/saufenbilder.384592}, title = {A numerical technique based on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points for solving functional integro-differential equations involving variable delays}, key = {cite}, author = {Kürkçü, Ömür Kıvanç and Gümgüm, Sevin and Baykuş Savaşaneril, Nurcan and Sezer, Mehmet} } APA Gümgüm, S , Baykuş Savaşaneril, N , Kürkçü, Ö , Sezer, M . (2018). A numerical technique based on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points for solving functional integro-differential equations involving variable delays. Sakarya University Journal of Science, 22 (6), 1659-1668. DOI: 10.16984/saufenbilder.384592 MLA Gümgüm, S , Baykuş Savaşaneril, N , Kürkçü, Ö , Sezer, M . "A numerical technique based on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points for solving functional integro-differential equations involving variable delays". Sakarya University Journal of Science 22 (2018): 1659-1668 Chicago Gümgüm, S , Baykuş Savaşaneril, N , Kürkçü, Ö , Sezer, M . "A numerical technique based on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points for solving functional integro-differential equations involving variable delays". Sakarya University Journal of Science 22 (2018): 1659-1668 RIS TY - JOUR T1 - A numerical technique based on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points for solving functional integro-differential equations involving variable delays AU - Sevin Gümgüm , Nurcan Baykuş Savaşaneril , Ömür Kıvanç Kürkçü , Mehmet Sezer Y1 - 2018 PY - 2018 N1 - doi: 10.16984/saufenbilder.384592 DO - 10.16984/saufenbilder.384592 T2 - Sakarya University Journal of Science JF - Journal JO - JOR SP - 1659 EP - 1668 VL - 22 IS - 6 SN - 1301-4048-2147-835X M3 - doi: 10.16984/saufenbilder.384592 UR - http://dx.doi.org/10.16984/saufenbilder.384592 Y2 - 2018 ER - EndNote %0 Sakarya University Journal of Science A numerical technique based on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points for solving functional integro-differential equations involving variable delays %A Sevin Gümgüm , Nurcan Baykuş Savaşaneril , Ömür Kıvanç Kürkçü , Mehmet Sezer %T A numerical technique based on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points for solving functional integro-differential equations involving variable delays %D 2018 %J Sakarya University Journal of Science %P 1301-4048-2147-835X %V 22 %N 6 %R doi: 10.16984/saufenbilder.384592 %U 10.16984/saufenbilder.384592 ISNAD Gümgüm, Sevin , Baykuş Savaşaneril, Nurcan , Kürkçü, Ömür Kıvanç , Sezer, Mehmet . "A numerical technique based on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points for solving functional integro-differential equations involving variable delays". Sakarya University Journal of Science 22 / 6 (Aralık 2018): 1659-1668. http://dx.doi.org/10.16984/saufenbilder.384592