一维无界域上热传导方程的有限元方法研究-study on finite element method of heat conduction equation in one-dimensional unbounded domain.docxVIP
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一维无界域上热传导方程的有限元方法研究-study on finite element method of heat conduction equation in one-dimensional unbounded domain
??旱|司??????上???????⑤???????工?????其?◆多??????????⑩④单??????上?????????(Schro¨dinger)??就?◆?????恒⑤?????粒????●??其????就▲??粒??????出②?????上????度?????上?????????????????◆力?和??数??其?????????????度?????????这????数?????????????????熟????④都不???????这?????????????出???数??④??????上???????⑤??⑩④ 单??④?????????????????????上????????上??④ 单??????⑩后?????上?数??????????????数???就?▲????????????????????????因????④???????????④??⑩??④[17, 45]??????????上????其单????延???→????????????→多??⑧数??数?统???统??????殊????才????????④?????④[26]?又→??????④???????上?⑧?数满???????????出???似???④?其????布??????上???⑩??④?????④???数????很多??????数??⑤??数矩?通⑦???疏???⑩??④????数矩???疏?????④很????????上???????⑤??????④??工???④?其???????? 引?????工??????工??上?出????????????将???上???④③????上?????何??出??度??工???????④③后????????度??????????④????????上????④???工???④??????⑩?⑩?????④?????上??????初???期???????椭????[11, 22, 23, 27]?对???? 上?物?????厚??D.Givoli??[15, 19]?出?????工?????建立????工???④???散??????出?数??⑦??????论?析????????[44]?出????工???④???散??????论?析????????上? 物????其?研??????参??③[16, 35]?就???⑧?????工???④?????上?物????????研?工???都?采??⑩???④??散??????量??很?????⑩??④??散???量?????????⑩?????◆误??析???对?????上??????????工???④??Crank ? N icolson????和??????⑩??④???散??????量和???量???[24]???④?散?工??????建???????散?????▲严???论?析?②????????散??????????????????◆误????对????L13⑧(τ, h)?m?(m = 1, 2)?⑩????Hs?数(s = 0, 1)???◆误??O[h?(s+ 2 )(hm+ 2 +3τ 2 )]?????◆?排????????章????论????引??工????出?工????????章????散?⑩????????章?析?⑩???????和?敛????章???上??????其?工??????⑧????初??????ψ(x, t)?t??2ψ(x, t)?x2= f (x, t), ?1 x +∞, 0 t +∞ ,(2.1)ψ(x, 0) = φ(x),x ∈ [?1, +∞) ,(2.2)ψ(?1, t) = β(t),t ∈ [0, +∞)(2.3)ψ(x, t) → 0,? x → +∞ ? ,(2.4)其?f (x, t)?φ(x)和β(t)?????数, φ(?1) = β(0)?f (x, t)??⑤?属??0 = {(x, t) |?1 ≤ x 0, 0 ≤ t +∞}?φ(x)??⑤?Supp{φ(x)} ? [?1, 0)??????(2.1) ?(2.4)?数?????引????工??Γ0 = {(x, t) | x = 0, 0 ≤ t +∞}?这???[?1, +∞) × [0, +∞)???两部????????0和??????e = {(x, t) | 0 ≤x +∞, 0 ≤ t +∞}?????e上?f (x, t) ≡ 0?φ(x) ≡ 0?②????⑧???(2.1) ? (2.4)??????e上?⑩?????ψ(x, t)满???ψ?2ψ?t ? ?x2 = 0,(x, t) ∈ ?e,(2.5)ψ(x, 0) = 0,x ∈ [0, +∞),(2.6)ψ → 0
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