光華講壇——社會(huì)名流與企業(yè)家論壇第6697期
主題：L1 method for multi-singularity problems arising from time delay fractional equations (關(guān)于帶多點(diǎn)奇異性的時(shí)間分?jǐn)?shù)階微分方程的L1數(shù)值算法)
主講人：澳門(mén)大學(xué)數(shù)學(xué)系 黃錫榮教授
主持人：數(shù)學(xué)學(xué)院 呂品教授
時(shí)間：12月24日10:30
地點(diǎn)：柳林校區(qū)通博樓B412會(huì)議室
主辦單位：數(shù)學(xué)學(xué)院 科研處
主講人簡(jiǎn)介：
黃錫榮，澳門(mén)大學(xué)數(shù)學(xué)系教授，主要研究領(lǐng)域?yàn)槠⒎址匠虜?shù)值解和數(shù)值代數(shù)。在SIMAX、JCP、JSC、JDE等知名SCI期刊上發(fā)表100余篇論文。曾獲多項(xiàng)澳門(mén)自然科學(xué)獎(jiǎng)、擔(dān)任SIAM東亞分會(huì)執(zhí)行委員會(huì)委員和秘書(shū)等。
內(nèi)容提要：
In this talk, we study delay fractional equations. We show that that the regularity of the solution at s+ is better than that at 0+, where s is a constant time delay. Improved regularity of the solution is obtained by the decomposition technique and a fitted L1 numerical scheme is designed for it. We then construct a corrected L1 scheme, of which optimal convergence order reaches 2-α, where α∈(0, 1) is the order of the Caputo derivative. Significantly, the correction terms share the same forms as the discrete convolution structure for the derivative, which implies that the computation and analysis of these two parts can be integrated together. Finally, error pointwise estimates of L1 method for delay fractional equations are derived by discrete Laplace transform method.
本報(bào)告討論的是分?jǐn)?shù)階延遲微分方程。我們發(fā)現(xiàn)了該方程的解在延遲點(diǎn)s+處比在0+點(diǎn)處有更好的正則性表現(xiàn)。結(jié)合改進(jìn)的正則性理論，我們研究了一個(gè)恰當(dāng)?shù)腖1數(shù)值算法。同時(shí)，我們構(gòu)建了一個(gè)具有最優(yōu)的2-α階的校正型L1算法，并結(jié)合離散Laplace變換對(duì)相應(yīng)算法進(jìn)行了誤差分析。
