Bu çalışmanın amacı homotopi analiz metodunu kullanarak gecikmeli diferansiyel denklemlerin önemli bir bölümü olan pantograph denklemlerinin çözümlerini elde etmek ve gerçek çözümleri ile karsllaştırmasını yapmaktır. Dört bölümden oluşan bu çalışmanın birinci bölümünde Gecikmeli diferansiyel denklemlerin kullamm alanlarl hakkmda bilgi verilerek Pantograph denklemlerinin iineminden bahsedildi. !kinci bollimiinde gecikmeli diferansiyel denklemler ve buna bagh olarak Pantograph denklemlerin elde edili~i anlatlldl. Pantograph denklemlerinin ge~itlerinden bahsedildi. Uyiincii biiliimde Homotopi Analiz Metodu tamttlarak Pantograph denklemleri ile Multi-Pantograph Denklemlerinin deformasyon denklemlerinin elde edili~i anlattldl. Diirdiincii biiliimde homotopi analiz metodu kullanllarak Pantograph denklemlerinin tz yakmsakhk kontrol parametresine bagh seri yiiziimleri elde edildi. <;:iiziim serilerine uygun tz yakmsakhk kontrol parametresi belirlendi. Homotopi analiz metodu ile diger yontemlerin mukayeseleri yapllarak hata grafikleri yizildi. Anahtar Kelimeler: Homotopi Analiz Metotu; Pantograph Denklemler; Gecikmeli Diferansiyel Denklemler.
The aim of this study is, using the homotopy analysis method, to get the solution of pantograph equations which are important parts of delay differential equations and to compare them with their real solutions. In the first part of this study which consists of four sections, the usage of delay differential equations and the importance of Pantograph equations are explained. In the second part, delay differential equations and accordingly, how we get pantograph equations are mentioned. Types ofpantograph equations are added afterwards. In the third part, by introducing the homotopy analysis method, how we get deformation equations of multi-pantograph equations with pantograph equations has been explained. In the fourth part, usmg the homotopy analysis method, the serial solutions of pantograph equations depending on the nconvergence control parameter have been obtained. n convergence control parameter appropriate to the solution series has been determined. Finally, homotopy analysis method and the other methods have been compared and their error graphs have been drawn. Key Words: Homotopy Analysis Method; Pantograph Equations; Delay Differential Equations
