文摘
In this letter, we propose a fast matrix time-extrapolation algorithm to solve semilinear parabolic problems of Crank–Nicolson-based finite element scheme, which employs exact matrix values computed by integral at time levels d="mmlsi19" class="mathmlsrc">ext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302762&_mathId=si19.gif&_user=111111111&_pii=S0893965916302762&_rdoc=1&_issn=08939659&md5=4e7fc6c0332dc5ab13a15139c51eae51" title="Click to view the MathML source">mer hidden">de">, d="mmlsi20" class="mathmlsrc">ext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302762&_mathId=si20.gif&_user=111111111&_pii=S0893965916302762&_rdoc=1&_issn=08939659&md5=6995d5ed613324b5c0b0b8d13427522a" title="Click to view the MathML source">m+per hidden">de">, d="mmlsi21" class="mathmlsrc">ext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302762&_mathId=si21.gif&_user=111111111&_pii=S0893965916302762&_rdoc=1&_issn=08939659&md5=68179437cace877c1c0a94f2d01a7a96" title="Click to view the MathML source">m+2per hidden">de"> to construct quadratic interpolation so that we can estimate matrix values at levels d="mmlsi22" class="mathmlsrc">ext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302762&_mathId=si22.gif&_user=111111111&_pii=S0893965916302762&_rdoc=1&_issn=08939659&md5=3c64f83b14c86bb61f2131ca8096c0c1" title="Click to view the MathML source">m+2p+1,m+2p+2,…,m+3p−1er hidden">de">, then the matrix value is recalculated at the level d="mmlsi23" class="mathmlsrc">ext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302762&_mathId=si23.gif&_user=111111111&_pii=S0893965916302762&_rdoc=1&_issn=08939659&md5=7a9f614be85b946bae1cc7b88476ee11" title="Click to view the MathML source">m+3per hidden">de">. This process is performed iteratively, and finally, the calculation for matrices decreases to d="mmlsi24" class="mathmlsrc">ext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302762&_mathId=si24.gif&_user=111111111&_pii=S0893965916302762&_rdoc=1&_issn=08939659&md5=13d6da0b6ceff25c118663b54e100aac" title="Click to view the MathML source">1∕per hidden">de">. The error estimate of this algorithm is proven, and numerical examples are established to support this theory.