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## A fitted approximate method for a Volterra delay-integro-differential equation with initial layer

#### Gabil M. Amiraliyev [1] , Ömer Yapman [2] , Mustafa Kudu [3]

This study is concerned with the finite-difference solution of singularly perturbed initial value problem for a linear first order Volterra integro-differential equation with delay. The method is based on the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. The emphasis is on the convergence of numerical method. It is shown that the method displays uniform convergence in respect to the perturbation parameter. Numerical results are also given.
Volterra delay-integro-differential equation, singular perturbation, finite difference, uniform convergence
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Birincil Dil en Matematik Matematik Orcid: 0000-0001-6585-7353Yazar: Gabil M. Amiraliyev (Sorumlu Yazar) Orcid: 0000-0003-3117-2932Yazar: Ömer Yapman Orcid: 0000-0002-6610-0587Yazar: Mustafa Kudu Yayımlanma Tarihi : 8 Ekim 2019
 Bibtex @araştırma makalesi { hujms629902, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2019}, volume = {48}, pages = {1417 - 1429}, doi = {}, title = {A fitted approximate method for a Volterra delay-integro-differential equation with initial layer}, key = {cite}, author = {Amiraliyev, Gabil M. and Yapman, Ömer and Kudu, Mustafa} } APA Amiraliyev, G , Yapman, Ö , Kudu, M . (2019). A fitted approximate method for a Volterra delay-integro-differential equation with initial layer. Hacettepe Journal of Mathematics and Statistics , 48 (5) , 1417-1429 . Retrieved from https://dergipark.org.tr/tr/pub/hujms/issue/49321/629902 MLA Amiraliyev, G , Yapman, Ö , Kudu, M . "A fitted approximate method for a Volterra delay-integro-differential equation with initial layer". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1417-1429 Chicago Amiraliyev, G , Yapman, Ö , Kudu, M . "A fitted approximate method for a Volterra delay-integro-differential equation with initial layer". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1417-1429 RIS TY - JOUR T1 - A fitted approximate method for a Volterra delay-integro-differential equation with initial layer AU - Gabil M. Amiraliyev , Ömer Yapman , Mustafa Kudu Y1 - 2019 PY - 2019 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1417 EP - 1429 VL - 48 IS - 5 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics A fitted approximate method for a Volterra delay-integro-differential equation with initial layer %A Gabil M. Amiraliyev , Ömer Yapman , Mustafa Kudu %T A fitted approximate method for a Volterra delay-integro-differential equation with initial layer %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 5 %R %U ISNAD Amiraliyev, Gabil M. , Yapman, Ömer , Kudu, Mustafa . "A fitted approximate method for a Volterra delay-integro-differential equation with initial layer". Hacettepe Journal of Mathematics and Statistics 48 / 5 (Ekim 2019): 1417-1429 . AMA Amiraliyev G , Yapman Ö , Kudu M . A fitted approximate method for a Volterra delay-integro-differential equation with initial layer. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1417-1429. Vancouver Amiraliyev G , Yapman Ö , Kudu M . A fitted approximate method for a Volterra delay-integro-differential equation with initial layer. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1429-1417.