Numerical Computation on Continuation of the Solution for the One-Dimensional Heat Equation(Scientific Computation and Numerical Analysis, <Special Issue> Joint Symposium of JSIAM Activity Groups 2007)

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  • 空間1次元熱伝導方程式の解の接続の数値計算(科学技術計算と数値解析,<特集>平成19年研究部会連合発表会)
  • 空間1次元熱伝導方程式の解の接続の数値計算
  • クウカン 1ジゲン ネツ デンドウ ホウテイシキ ノ カイ ノ セツゾク ノ スウチ ケイサン

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Abstract

We consider a problem governed by the simple one-dimensional heat equation. In our problem two parameters are introduced. One is for the determination of the initial boundary value problem, the continuation problem or the initial value problem. Another one is for analiticity. Numerical simulations are carried out by using two different numerical methods(FDM⊕EE and IPNS). Numerical results are interesting as follows: Both methods give similar results converging to the smooth solution for the initial value problem which has non-uniqueness of the solution. Moreover, both methods give different results for the continuation problem.

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