کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4633611 1340674 2009 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation
چکیده انگلیسی

In this paper, we consider the variable-order nonlinear fractional diffusion equation∂u(x,t)∂t=B(x,t)xRα(x,t)u(x,t)+f(u,x,t),where xRα(x,t)xRα(x,t) is a generalized Riesz fractional derivative of variable order α(x,t)(1<α(x,t)⩽2) and the nonlinear reaction term f(u,x,t)f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|⩽L|u1-u2||f(u1,x,t)-f(u2,x,t)|⩽L|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 212, Issue 2, 15 June 2009, Pages 435–445
نویسندگان
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