کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5776719 | 1632159 | 2017 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Smoothing transformation and spline collocation for weakly singular Volterra integro-differential equations
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات محاسباتی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Smoothing transformation and spline collocation for weakly singular Volterra integro-differential equations Smoothing transformation and spline collocation for weakly singular Volterra integro-differential equations](/preview/png/5776719.png)
چکیده انگلیسی
This work is concerned with the construction and analysis of high order numerical methods for solving initial value problems for linear Volterra integro-differential equations with different types of singularities. Using an integral reformulation of the initial value problem, a smoothing transformation is applied so that the exact solution of the resulting equation does not contain any singularities in its derivatives up to a certain order. After that, the regularized equation is solved by a piecewise polynomial collocation method on a uniform or mildly graded grid. Finally, the obtained spline approximations can be used to define (typically non-polynomial) approximations for the initial value problem. The theoretical results are tested by some numerical examples.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Numerical Mathematics - Volume 114, April 2017, Pages 63-76
Journal: Applied Numerical Mathematics - Volume 114, April 2017, Pages 63-76
نویسندگان
T. Diogo, P.M. Lima, A. Pedas, G. Vainikko,