Local Annihilation Method and Some Stiff Problems
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
A. Abdollahi
1
,
E. Babolian
2
1 - Department of Mathematics, Maragheh Branch, Islamic Azad University, Maragheh, Iran.
2 - Department of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran.
کلید واژه: Residual function, Stiff problems, Ill-posed problems, Local annihilation method,
چکیده مقاله :
In this article, a new scheme inspired from collocation method is presented for numerical solution of stiff initial-value problems and Fredholm integral equations of the first kind based on the derivatives of residual function. Then, the error analysis of this method is investigated by presenting an error bound. Numerical comparisons indicate that the presented method yields accurate approximations in many cases in which the collocation method is failed.
در این مقاله یک روش عددی جدید برگرفته از روش هممحلی، برای حل عددی مسایل مقدار اولیه سخت و معادلات انتگرال فردهلم نوع اول مبتنی بر مشتقات تابع مانده ارایه شده است؛ سپس تحلیل خطای این روش عددی با ارایه کران بالا برای خطا مورد بررسی قرار میگیرد. کارایی این روش با ارایه چندین مثال عددی از مسایل سخت و بدوضع با کارایی روش هممحلی مقایسه میشود. نتایج عددی بدست آمده نشان میدهد که روش ارایه شده در جایی که روش هممحلی برای حل عددی این نوع مسایل با شکست مواجه میشود از کارایی بالایی برخوردار است.
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