مشخصات پژوهش

عنوان	The numerical solution of weakly singular integral equations based on the meshless product integration (MPI) method with error analysis
نوع پژوهش	مقاله چاپ‌شده در مجلات علمی
کلیدواژه‌ها	Fredholm integral equation; Volterra integral equation; Weakly singular kernel; Radial basis function; Meshless method; Product integration method; Error analysis
چکیده	This article investigates a numerical scheme based on radial basis functions (RBFs) for solving weakly singular integral equations by combining the product integration method and the collocation method. The RBF methodology is an effective technique for the approximation of an unknown function by using a set of scattered points. Since the proposed scheme does not require any background mesh for its approximation and numerical in- tegration unlike other product integration methods, it is called the meshless product integration (MPI) method. The proposed scheme is simple and computationally attractive. This approach reduces the solution of the weakly singular integral equation to the solution of a linear system of algebraic equations. The error analysis of the method is provided. The validity and efficiency of the new technique are demonstrated through several tests.
پژوهشگران	پوریا عصاری (نفر اول)، حجت اله ادیبی (نفر دوم)، مهدی دهقان (نفر سوم)