کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4635495 | 1340712 | 2007 | 9 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A simplification to Fredholm's solution to the Fredholm integral equation of the second kind
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Fredholm's classic solution to his linear integral equation of the second kind has been generally considered to be too complex to provide a practical solution method. It gives the resolvent kernel as a ratio of two infinite series, with terms in each series containing multiple integrals of determinants such that the evaluation of the nth term would seem to require n! different n-fold multi-integrations, a formidable task even for modest values of n. This paper shows, however, that by using the methods of the combinatorics of permutations and by solving a well-known recursion relation, Fredholm's solution can be simplified considerably, In this simplified form, the nth term of each series requires the evaluation of just one new multi-integral. Thus presented is a new expression for the Fredholm's solution, and the practical use of this expression is demonstrated on some example problems.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 189, Issue 2, 15 June 2007, Pages 1078-1086
Journal: Applied Mathematics and Computation - Volume 189, Issue 2, 15 June 2007, Pages 1078-1086
نویسندگان
K.G. Terry Hollands,