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Solving Second Kind Volterra-Fredholm Integral Equations by Using Triangular Functions (TF) and Dynamical Systems | ||
| Control and Optimization in Applied Mathematics | ||
| مقاله 4، دوره 2، شماره 1، تیر 2017، صفحه 43-63 اصل مقاله (696.11 K) | ||
| نوع مقاله: Applied Article | ||
| نویسندگان | ||
| Azhdar Soleymanpour Bakefayat* 1؛ Sima Karamseraji2 | ||
| 1Department of Mathematics, Farhangian University, Tehran, Iran | ||
| 2Department of Mathematics, Karaj Branch, Islamic Azad University, Alborz, Iran | ||
| چکیده | ||
| The method of triangular functions (TF) could be a generalization form of the functions of block-pulse (Bp). The solution of second kind integral equations by using the concept of TF would lead to a nonlinear equations system. In this article, the obtained nonlinear system has been solved as a dynamical system. The solution of the obtained nonlinear system by the dynamical system through the Newton numerical method has got a particular priority, in that, in this method, the number of the unknowns could be more than the number of equations. Besides, the point of departure of the system could be an infeasible point. It has been proved that the obtained dynamical system is stable, and the response of this system can be achieved by using of the fourth order Runge-Kutta. The results of this method is comparable with the similar numerical methods; in most of the cases, the obtained results by the presented method are more efficient than those obtained by other numerical methods. The efficiency of the new method will be investigated through examples. | ||
| کلیدواژه‌ها | ||
| Second kind Fredholm-Volterra integral equations؛ Nonlinear systems؛ Dynamical systems؛ Triangular functions؛ Block-pulse functions | ||
| عنوان مقاله [English] | ||
| حل معادلات انتگرال ولترا-فردهلم نوع دوم با استفاده از توابع مثلثی و سیستم‌های دینامیکی | ||
| نویسندگان [English] | ||
| اژدر سلیمانپور باکفایت1؛ سیما کرم سراجی2 | ||
| 1استادیار ریاضی کاربردی، تهران، دانشگاه فرهنگیان، گروه ریاضی | ||
| 2دانشجوی دکتری ریاضی کاربردی، البرز، دانشگاه آزاد اسلامی واحد کرج | ||
| چکیده [English] | ||
| روش توابع مثلثی می‌تواند تعمیمی از روش بلاک پالس باشد. جواب معادلات انتگرال نوع دوم با استفاده از روش توابع مثلثی، به یک دستگاه معادلات غیرخطی منجر می‌شود. در این مقاله، دستگاه غیرخطی حاصل توسط یک سیستم دینامیکی حل شده است. حل دستگاه غیرخطی حاصل از روش سیستم‌های دینامیکی نسبت به روش عددی نیوتن دارای این مزیت است که در این روش تعداد مجهولات می‌تواند از تعداد معادلات بیشتر باشد. همچنین نقطه شروع سیستم می‌تواند نشدنی باشد. ثابت شده است که سیستم دینامیکی حاصل، پایدار بوده و پاسخ این سیستم از روش عددی رانگ کوتای مرتبه 4 حاصل می‌شود. نتایج حاصل قابل مقایسه با نتایج روش‌های عددی مشابه است و در اکثر حالات نتایج بدست آمده بهتر از نتایج روش‌های عددی دیگر است. تاثیر روش جدید با ذکر مثال‌هایی بررسی شده است. | ||
| کلیدواژه‌ها [English] | ||
| معادلات انتگرال فردهلم-ولترا, سیستم‌های غیرخطی, سیستم‌های دینامیکی, توابع مثلثی, توابع بلاک پالس | ||
| مراجع | ||
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