Projection and multi-projection methods for second kind Volterra-Hammerstein integral equation
سال انتشار: 1400
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 137
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شناسه ملی سند علمی:
JR_IJNAA-12-2_021
تاریخ نمایه سازی: 11 آذر 1401
چکیده مقاله:
In this article, we discuss the piecewise polynomial based Galerkin method to approximate the solutions of second kind Volterra-Hammerstein integral equations. We discuss the convergence of the approximate solutions to the exact solutions and obtain the orders of convergence \mathcal O(h^{r}) and \mathcal O(h^{۲r}), respectively, for Galerkin and its iterated Galerkin methods in uniform norm, where h, ~r denotes the norm of the partition and smoothness of the kernel, respectively. We also obtain the superconvergence results for multi-Galerkin and iterated multi-Galerkin methods. We show that iterated multi-Galerkin method has the order of convergence \mathcal O(h^{۳r}) in the uniform norm. Numerical results are provided to demonstrate the theoretical results.
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نویسندگان
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Assistant Professor, Department of Mathematics, Indian Institute of Technology Jodhpur, Rajasthan-۳۴۲۰۳۷, India.
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Department of Mathematics Indian Institute of Technology Kharagpur, Kharagpur - ۷۲۱ ۳۰۲, India
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Department of Mathematics Indian Institute of Technology Kharagpur, Kharagpur - ۷۲۱ ۳۰۲, India