کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1705686 | 1012438 | 2011 | 11 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations](/preview/png/1705686.png)
In this paper, we state and prove a new formula expressing explicitly the derivatives of shifted Chebyshev polynomials of any degree and for any fractional-order in terms of shifted Chebyshev polynomials themselves. We develop also a direct solution technique for solving the linear multi-order fractional differential equations (FDEs) with constant coefficients using a spectral tau method. The spatial approximation with its fractional-order derivatives (described in the Caputo sense) are based on shifted Chebyshev polynomials TL,n(x) with x ∈ (0, L), L > 0 and n is the polynomial degree. We presented a shifted Chebyshev collocation method with shifted Chebyshev–Gauss points used as collocation nodes for solving nonlinear multi-order fractional initial value problems. Several numerical examples are considered aiming to demonstrate the validity and applicability of the proposed techniques and to compare with the existing results.
Journal: Applied Mathematical Modelling - Volume 35, Issue 12, December 2011, Pages 5662–5672