کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
11017692 | 1722375 | 2019 | 23 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A high-order L2-compact difference method for Caputo-type time-fractional sub-diffusion equations with variable coefficients
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
A high-order compact finite difference method is proposed for solving a class of time-fractional sub-diffusion equations. The diffusion coefficient of the equation may be spatially variable and the time-fractional derivative is in the Caputo sense with the order αâ¯ââ¯(0, 1). The Caputo time-fractional derivative is discretized by a (3âα) th-order numerical formula (called the L2 formula here) which is constructed by piecewise quadratic interpolating polynomials but does not require any sub-stepping scheme for the approximation at the first-time level. The variable coefficient spatial differential operator is approximated by a fourth-order compact finite difference operator. By developing a technique of discrete energy analysis, a full theoretical analysis of the stability and convergence of the method is carried out for the general case of variable coefficient and for all αâ¯ââ¯(0, 1). The optimal error estimate is obtained in the L2 norm and shows that the proposed method has the temporal (3âα) th-order accuracy and the spatial fourth-order accuracy. Further approximations are also considered for enlarging the applicability of the method while preserving its high-order accuracy. Applications are given to three model problems, and numerical results are presented to demonstrate the theoretical analysis results.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 342, 1 February 2019, Pages 71-93
Journal: Applied Mathematics and Computation - Volume 342, 1 February 2019, Pages 71-93
نویسندگان
Yuan-Ming Wang, Lei Ren,