Analysis of second order difference schemes on non-uniform grids for quasilinear parabolic equations

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• 作者：Piotr Matus^a ; ^b ; ^{matus@im.bas-net.by" class="auth_mail" title="E-mail the corresponding author} ; Le Minh Hieu^c ; ^d ; ^{leminhhieuktdn@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Lubin G. Vulkov^e ; ^{lvalkov@un-ruse.bg" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Maximum principle ; Monotone difference scheme ; Quasilinear parabolic equation ; Gamma equation
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：310
• 期：Complete
• 页码：186-199
• 全文大小：474 K

文摘

On the base of the maximum principles two-sided estimates for solutions of difference schemes are proved without any assumption of sign-definiteness of input data. Second order unconditional monotone difference scheme for quasilinear convection–diffusion equation on uniform grids is constructed. A priori estimates of the difference solution on uniform norm class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716301716&_mathId=si21.gif&_user=111111111&_pii=S0377042716301716&_rdoc=1&_issn=03770427&md5=976bb837197ede9f42afb6ad5b8a1cd4" title="Click to view the MathML source">Cclass="mathContainer hidden">class="mathCode">$C$ are established. The obtained results are generalized for the case of non-uniform spatial grids. Numerical experiments confirming theoretical results are presented.