Three-Dimensional Nonlinear Integral Operator with the Modelling of Majorant Function

 تقدم هذه الورقة البحثية طريقة  لايجاد الحل التقريبي لمؤثر فولتيرا التكاملي  الثلاثي الأبعاد غير الخطي في  R3. حيث يتم استخدام مفهوم (Majorant function) وباستخدام طريقة نيوتن المعدلة  لتحويل مؤثر فولتيرا التكاملي  الثلاثي الأبعاد غير الخطي  إلى متتالية  لمؤثر فولتيرا التكاملي  الثلاثي الأبعاد الخطي ومن يتم استخدام طريقة (Gaussian-Legendre)  التربيعية لايجاد الحل التقريبي لمؤثر فولتيرا التكاملي  الثلاثي الأبعاد الخطي من خلال التعامل مع نظام جبري خطي.تم مناقشة وجود ووحدانية الحل للطريقة المستخدمة مع اعطاء أمثلة توضيحية لإظهار دقة وكفاءة الطريقة.In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R3 is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model. Mathematical Subject Classification (2010):  45P05, 45G10, 47H9

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