本文選題：Allen-Cahn方程 + 有限差分　； 參考：《福州大學(xué)學(xué)報(bào)(自然科學(xué)版)》2017年03期

【摘要】：利用一階有限差分-譜方法求解Allen-Cahn方程u_t-Δu+1/(ε~2)f(u)=0并進(jìn)行嚴(yán)格的誤差分析,其中交面寬度ε是一個(gè)很小的參數(shù).誤差分析結(jié)果表明:若初始解u_0的正則性受ε~(-σ)控制,當(dāng)時(shí)間步長(zhǎng)δt充分小以及多項(xiàng)式階數(shù)N充分大時(shí),全離散格式的誤差界也受ε~(-σ)控制.該誤差分析有效改進(jìn)了誤差界受1/e~(ε~2)控制的結(jié)果.
[Abstract]:By using a finite difference spectrum method to solve Allen-Cahn equation u_t- u+1/ (~2) f (U) =0 and the strict error analysis, the width of epsilon is a small parameter. The error analysis results show that if the initial solution u_0 regularity by ~ (- epsilon sigma control) and when the time step length delta T is sufficiently small and the polynomial order N is sufficiently large, the error bound of the fully discrete scheme is also affected by the E ~ (- Sigma) control. Analysis effectively improves the error bound of the error by 1/e~ (~2) control results.

【作者單位】： 福州大學(xué)數(shù)學(xué)與計(jì)算機(jī)科學(xué)學(xué)院;
【基金】：福建省教育廳科技資助項(xiàng)目(JA14034) 福建省自然科學(xué)基金資助項(xiàng)目(2016J01013)
【分類號(hào)】：O241.8
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本文編號(hào)：1734404