講座主題：Efficient sixth order finite difference method for the nonlinear wave equation with variable coefficients
專家姓名：葛永斌
工作單位：大連民族大學(xué)
講座時(shí)間：2024年04月20日10:20-10:50
講座地點(diǎn)：數(shù)學(xué)與信息科學(xué)學(xué)院341
主辦單位：煙臺大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)容摘要：
In this study, firstly, a sixth-order finite difference operator and correction technique of truncation error remainder are employed to construct a nonlinear high-order finite difference scheme and a linearized high-order finite difference scheme for solving the numerical solution of two-dimensional nonlinear wave equations with variable coefficients. Both new schemes have sixth-order accuracy in space and fourth-order accuracy in time. Then, the Richardson extrapolation technique is applied to obtain a numerical solution of sixth-order accuracy in both time and space. Meanwhile, the stability of the corresponding difference scheme for the linear wave equation is proved by Fourier analysis. In addition, two proposed sixth-order schemes are extended to solve the three-dimensional nonlinear wave equation. Finally, some numerical experiments are presented to confirm the effectiveness and accuracy of the proposed method.
主講人介紹：
葛永斌,，男,，漢族，寧夏青銅峽市人。2000年寧夏大學(xué)應(yīng)用數(shù)學(xué)專業(yè)碩士研究生畢業(yè),，獲理學(xué)碩士學(xué)位。2004年3月上海理工大學(xué)工程熱物理專業(yè)博士研究生畢業(yè),，獲得工學(xué)博士學(xué)位?，F(xiàn)為大連民族大學(xué)理學(xué)院教授、寧夏大學(xué)兼職博士生導(dǎo)師,。2010年5月至2011年5在美國肯塔基大學(xué)作訪問學(xué)者,。2020年12月入選寧夏自治區(qū)青年拔尖人才工程。目前主要從事計(jì)算數(shù)學(xué),、計(jì)算流體力學(xué),、計(jì)算生物學(xué)和數(shù)學(xué)軟件開發(fā)方面的研究。先后主持國家自然科學(xué)基金項(xiàng)目5項(xiàng),，其中面上項(xiàng)目和青年項(xiàng)目各1項(xiàng),，地區(qū)項(xiàng)目3項(xiàng)。主持教育部科學(xué)技術(shù)研究重點(diǎn)項(xiàng)目,、霍英東教育基金會高校青年教師基金項(xiàng)目,、寧夏自然科學(xué)基金重點(diǎn)項(xiàng)目、寧夏自治區(qū)重點(diǎn)研發(fā)項(xiàng)目等若干項(xiàng),。在核心以上級別刊物上發(fā)表學(xué)術(shù)論文130余篇,，其中被SCI檢索60余篇。
