حل عددی معادلات انتگرال ولترا-فردهلم غیرخطی نوع اول با استفاده از چندجمله‌ای‌های لژاندر جایگزین

نویسندگان
سهراب بزم 1
علیرضا حسینی 2
1 دانشگاه مراغه
2 دانشگاه تهران
10.52547/mmr.7.3.443
چکیده
در این مقاله، چندجمله­ ای­ های لژاندر جایگزین (ALPs) برای تقریب جواب معادلات انتگرال ولترا-فردهلم غیرخطی نوع اول (VFIEs) استفاده شده­ اند. ابتدا مساله به یک معادله انتگرال ولترا-فردهلم نوع دوم تبدیل می­ شود و سپس، با استفاده از ماتریس­ های عملیاتی انتگرال­ گیری و حاصل ضرب ALP، حل مساله ثانوی به حل یک دستگاه از معادلات جبری غیرخطی، که مجهولات آن ضرایب ALP جواب دقیق مساله هستند، کاهش می­ یابد. یک تحلیل خطا برای روش ارائه شده انجام شده است و نتایج مثال­ های عددی نشان می­ دهند که این روش، حتی در صورت استفاده از تعداد کمی ازALPs دقت خوبی ارائه می­ دهد.
کلیدواژه‌ها
معادلات انتگرال غیرخطی نوع اول
معادلات انتگرال ولترا-فردهلم
چندجمله‌ای‌های لژاندر جایگزین
ماتریس‌عملیاتی

عنوان مقاله English

Numerical solution of nonlinear Volterra-Fredholm integral equations of the first kind using alternative Legendre polynomials

نویسندگان English

Sohrab Bazm 1
Alireza Hosseini 2
1 University of Maragheh
2 University of Tehran
چکیده English

Alternative Legendre polynomials (ALPs) are used for approximating the solution of nonlinear Volterra-Fredholm integral equations (VFIEs) of the rst kind. The problem is rst transformed into a second kind VFIE and then, using the ALP operational matrices of integration and the product, the solution of the later problem is reduced to the one of solving a system of nonlinear algebraic equations with unknown ALP coecients of the exact solution. An error analysis of the method is given. Results of numerical examples are presented, which illustrate that the proposed method achieve good accuracy even using a small number of ALPs.

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کلیدواژه‌ها English

Nonlinear integral equations of the first kind
Volterra-Fredholm integral equations
Alternative Legendre polynomials
Operational matrix
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