非線性分?jǐn)?shù)階微分方程的hp 型Legendre 譜配置法
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摘要：研究了求解非線性分?jǐn)?shù)階微分方程的 hp 型 Legendre 譜配置法。首先提出將多分?jǐn)?shù)階微分方程轉(zhuǎn)化成等價(jià)的 Volterra 積分方程， 其次構(gòu)造了近似求解原方程的數(shù)值方法， 最后通過(guò)數(shù)值實(shí)驗(yàn)說(shuō)明了該算法的理論正確性以及所構(gòu)造數(shù)值方法的有效性。
關(guān)鍵詞：非線性分?jǐn)?shù)階微分方程;Legendre 譜配置法;hp 型誤差界
中圖分類(lèi)號(hào)：O 175 文獻(xiàn)標(biāo)志碼：A
An hp-version Legendre spectral collocation method for nonlinear fractional differential equations
LI Shan， AN Xiao， SUN Guilei
（College of Science， University of Shanghaifor Science and Technology， Shanghai 200093， China）
Abstract： The hp-version Legendre spectral collocation method for solving nonlinear fractionaldifferential equations was studied. At first， the multifractional differential equation was transformed intoan equivalent Volterra integral equation. Then a numerical method to approximate the original equationwas constructed. Finally， the correctness of the algorithm theory and the effectiveness of the proposednumerical method were demonstrated by numerical experiments.
Keywords： nonlinear fractional differential equations; Legendre spectral collocation method; hpversion error bounds
1 問(wèn)題的提出
分?jǐn)?shù)階微分方程最重要的是非局部性質(zhì)， 它能有效地避免整數(shù)階導(dǎo)數(shù)的局部性， 所以，分?jǐn)?shù)階導(dǎo)數(shù)可以更加精確地描述對(duì)歷史有依賴的問(wèn)題。（剩余5213字）