Recovering boundary data in planar heat conduction using a boundary integral equation method

Electronic Journal of Boundary Elements

关键词: Boundary Integral Equations, Cuchy Problem, Heat Equation;   

DOI  :  10.14713/ejbe.v9i1.1065

学科分类：农业科学（综合）

来源: Rutgers University Libraries

【 摘 要 】

We consider a Cauchy problem for the heat equation, where thetemperature field is to be reconstructed from the temperature and heatflux given on a part of the boundary of the solution domain. We employ aLandweber type method proposed in ~\cite{Bast}, where a sequence ofmixed well-posed problems are solved at each iteration step to obtain astable approximation to the original Cauchy problem. We develop anefficient boundary integral equation method for the numerical solutionof these mixed problems, based on the method of Rothe. Numericalexperiments are presented both with exact and noisy data, showing theefficiency and stability of the proposed procedure and approximations.

【 授权许可】

CC BY-NC