کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
520485 867722 2013 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A high order schema for the numerical solution of the fractional ordinary differential equations
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
A high order schema for the numerical solution of the fractional ordinary differential equations
چکیده انگلیسی

In this paper we present a general technique to construct high order schemes for the numerical solution of the fractional ordinary differential equations (FODEs). This technique is based on the so-called block-by-block approach, which is a common method for the integral equations. In our approach, the classical block-by-block approach is improved in order to avoiding the coupling of the unknown solutions at each block step with an exception in the first two steps, while preserving the good stability property of the block-by-block schemes. By using this new approach, we are able to construct a high order schema for FODEs of the order α,α>0α,α>0. The stability and convergence of the schema is rigorously established. We prove that the numerical solution converges to the exact solution with order 3+α3+α for 0<α⩽10<α⩽1, and order 4 for α > 1. A series of numerical examples are provided to support the theoretical claims.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 238, 1 April 2013, Pages 154–168
نویسندگان
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