Unformatted text preview: Î» Î» = 1 + k âˆ† t âˆ’ 2 r + 2 r cos Î² = 1 + 2 r (cos Î² âˆ’ 1  {z } = âˆ’ 2 sin 2 Î² 2 ) + k âˆ† t Î» = 1 âˆ’ 4 r sin 2 Î² 2 + k âˆ† t If r â‰¤ 1 2 then Î» â‰¤ 1 + O (âˆ† t ) The âˆ† t term makes sense since ku term allows the solution to grow in time and thus Î» (and the numerical solution) must be allowed to grow. 323...
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 Fall '08
 BELL,D
 Numerical Analysis, Partial differential equation, 1D Heat Equation, forwardtime diï¬€erence method

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