A New Method for Solving Multi-Dimensional Fredholm Integral Equations and Its Convergence Analysis
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
N. Mahmoodi ‎Darani‎
1
(Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.)
کلید واژه: Multi-dimensional linear and nonlinear, Fredholm Integral Equations, Multi-dimensional expansion, Convergence analysis, Boundary conditions,
چکیده مقاله :
In this paper, we focus on obtaining an approximate solution for multi-dimensional Fredholm integral equations of second kind. An expansion method is used for treatment multi-dimensional Fredholm integral equation of second kind. This method reduces multi-dimensional integral equation to a partial differential equation. After constructing boundary conditions, this partial differential equation reduces to algebraic equation that can be solved easily with any of the usual methods. Furthermore some theorems are proved for convergence analysis. Finally, for showing the efficiency of the method we use some numerical examples
در این تحقیق، توسعه یک راه حل تقریبی برای معادلات انتگرال فردهلم چند بعدی نوع دوم ارائه شده است. برای این منظور، روش بسط به کار برده شده است که منجر به تبدیل معادله انتگرال چندبعدی به یک معادله دیفرانسیل با مشتقات جزیی می شود. با ایجاد شرایط مرزی، این معادله با مشتقات جزیی، به یک معادله جبری تبدیل می شود که به آسانی و با روش‌های مستقیم قابل حل خواهد بود. همچنین به کمک چند تئوری، همگرایی این تحلیل اثبات خواهد شد. در انتها نیز کارایی این روش به کمک چند مثال عددی نشان داده خواهد شد.
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