本文選題：時間分布階和空間Riesz分數(shù)階擴散方程 + L2-1_σ插值格式　； 參考：《湘潭大學》2017年碩士論文

【摘要】：本文考慮一類時間分布階和空間Riesz分數(shù)階擴散方程初邊值問題的數(shù)值求解。首先,對分布階中的積分項用復化中矩形公式進行離散,這樣分布階分數(shù)階微分方程轉(zhuǎn)變成了多項的時間Caputo分數(shù)階擴散方程。然后,將方程中的多項時間Caputo導數(shù)用L2- 1σ插值格式進行離散,對空間Riesz分數(shù)階導數(shù)采用線性插值和分數(shù)階中心差商逼近,從而構(gòu)造了數(shù)值方法,并證明了方法的穩(wěn)定性和收斂性。該數(shù)值方法的收斂階為OO(τ2 +h2+ (△α)2),其中τ、h、△α分別表示時間步長、空間步長、分布階步長。數(shù)值實驗表明數(shù)值方法的理論分析和結(jié)果是一致的,也表明數(shù)值方法的有效性。
[Abstract]:In this paper, we consider the numerical solution of the initial boundary value problem for a class of diffusion equations of time distribution order and space Riesz fractional order. First, the integral term in the distribution order is discretized by the rectangular formula in the complex form, so that the fractional order differential equation of the distributed order is transformed into a multiterm Caputo fractional diffusion equation. Then, the multi-time Caputo derivatives in the equation are discretized by L _ 2-1 蟽 interpolation scheme, and the linear interpolation and fractional center difference quotient are used to approximate the fractional derivative of space Riesz, and the numerical method is constructed. The stability and convergence of the method are proved. The convergence order of the numerical method is O _ O (蟿 _ 2h _ 2 (偽 ~ + _ 2), where 蟿 _ h, 偽 denotes the time step, the space step and the distribution order step, respectively. Numerical experiments show that the theoretical analysis of the numerical method is consistent with the results, and the effectiveness of the numerical method is also demonstrated.
【學位授予單位】：湘潭大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O241.8

【參考文獻】

相關(guān)期刊論文 前1條

1 沈淑君,劉發(fā)旺;解分數(shù)階Bagley-Torvik方程的一種計算有效的數(shù)值方法[J];廈門大學學報(自然科學版);2004年03期

相關(guān)碩士學位論文 前1條

1 劉茜;兩類時間分布階擴散方程的差分方法[D];湘潭大學;2016年

，

本文編號：1958207