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## Lucas polynomial solution of nonlinear differential equations with variable delays

#### Sevin GÜMGÜM [1] , Nurcan BAYKUŞ SAVAŞANERİL [2] , Ömür Kıvanç KÜRKÇÜ [3] , Mehmet SEZER [4]

In this study, a novel matrix method based on Lucas series and collocation points has been used to solve nonlinear differential equations with variable delays. The application of the method converts the nonlinear equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Lucas coefficients. The method is tested on three problems to show that it allows both analytical and approximate solutions.

Nonlinear delay differential equations, Variable delays, Matrix and collocation methods, Lucas polynomials and series.
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Birincil Dil en Matematik Matematik Orcid: 0000-0002-0594-2377Yazar: Sevin GÜMGÜM (Sorumlu Yazar)Kurum: Izmir University of EconomicsÜlke: Turkey Orcid: 0000-0002-3098-2936Yazar: Nurcan BAYKUŞ SAVAŞANERİL Kurum: Dokuz Eylül ÜniversitesiÜlke: Turkey Orcid: 0000-0002-3987-7171Yazar: Ömür Kıvanç KÜRKÇÜ Kurum: Izmir University of EconomicsÜlke: Turkey Orcid: 0000-0002-7744-2574Yazar: Mehmet SEZER Kurum: MANISA CELAL BAYAR UNIVERSITYÜlke: Turkey Yayımlanma Tarihi : 2 Nisan 2020
 Bibtex @araştırma makalesi { hujms460975, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2020}, volume = {49}, pages = {553 - 564}, doi = {10.15672/hujms.460975}, title = {Lucas polynomial solution of nonlinear differential equations with variable delays}, key = {cite}, author = {GÜMGÜM, Sevin and BAYKUŞ SAVAŞANERİL, Nurcan and KÜRKÇÜ, Ömür Kıvanç and SEZER, Mehmet} } APA GÜMGÜM, S , BAYKUŞ SAVAŞANERİL, N , KÜRKÇÜ, Ö , SEZER, M . (2020). Lucas polynomial solution of nonlinear differential equations with variable delays. Hacettepe Journal of Mathematics and Statistics , 49 (2) , 553-564 . DOI: 10.15672/hujms.460975 MLA GÜMGÜM, S , BAYKUŞ SAVAŞANERİL, N , KÜRKÇÜ, Ö , SEZER, M . "Lucas polynomial solution of nonlinear differential equations with variable delays". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 553-564 Chicago GÜMGÜM, S , BAYKUŞ SAVAŞANERİL, N , KÜRKÇÜ, Ö , SEZER, M . "Lucas polynomial solution of nonlinear differential equations with variable delays". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 553-564 RIS TY - JOUR T1 - Lucas polynomial solution of nonlinear differential equations with variable delays AU - Sevin GÜMGÜM , Nurcan BAYKUŞ SAVAŞANERİL , Ömür Kıvanç KÜRKÇÜ , Mehmet SEZER Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.460975 DO - 10.15672/hujms.460975 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 553 EP - 564 VL - 49 IS - 2 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.460975 UR - https://doi.org/10.15672/hujms.460975 Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Lucas polynomial solution of nonlinear differential equations with variable delays %A Sevin GÜMGÜM , Nurcan BAYKUŞ SAVAŞANERİL , Ömür Kıvanç KÜRKÇÜ , Mehmet SEZER %T Lucas polynomial solution of nonlinear differential equations with variable delays %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 2 %R doi: 10.15672/hujms.460975 %U 10.15672/hujms.460975 ISNAD GÜMGÜM, Sevin , BAYKUŞ SAVAŞANERİL, Nurcan , KÜRKÇÜ, Ömür Kıvanç , SEZER, Mehmet . "Lucas polynomial solution of nonlinear differential equations with variable delays". Hacettepe Journal of Mathematics and Statistics 49 / 2 (Nisan 2020): 553-564 . https://doi.org/10.15672/hujms.460975 AMA GÜMGÜM S , BAYKUŞ SAVAŞANERİL N , KÜRKÇÜ Ö , SEZER M . Lucas polynomial solution of nonlinear differential equations with variable delays. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 553-564. Vancouver GÜMGÜM S , BAYKUŞ SAVAŞANERİL N , KÜRKÇÜ Ö , SEZER M . Lucas polynomial solution of nonlinear differential equations with variable delays. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 564-553.

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