INVERSE PROBLEMS IN PARTIAL DIFFERENTIAL EQUATIONS.
INVERSE PROBLEMS IN PARTIAL DIFFERENTIAL EQUATIONS.
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发表时间：
1968-08
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通讯作者：
D. Luckinbill;S. B. Childs
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作者：
D. Luckinbill;S. B. Childs
摘要：本文以拉普拉斯方程和非稳态热传导方程为例，说明了偏微分方程的辨识过程。求解的过程包括用差分算子代替除一个自变量外的所有自变量的偏导数。线性边值问题通过特解的叠加来求解。对于由方程的原始形式或由辨识过程引起的非线性边值问题，利用函数空间中的Newton-Raphson-Kantorovich展开式，将解化为求解线性边值问题的迭代过程。对于所考虑的问题，这个程序已被证明是有效的，并在一个合理的近似偏微分方程的边值问题的解决方案的结果。对于识别问题，它示出的常数参数被识别到相同的精度作为在识别过程中使用的补充数据。（作者）
Abstract : A procedure for identification in partial differential equations is described and illustrated by the Laplace equation and the unsteady heat conduction equation. The procedure for solution involves the substitution of difference operators for the partial derivatives with respect to all but one of the independent variables. The linear boundary value problem is solved by superposition of particular solutions. For non-linear boundary value problems which arise from the original form of the equation or from the identification procedure, a Newton-Raphson-Kantorovich expansion in function space is used to reduce the solution to an iterative procedure of solving linear boundary value problems. For the problems considered, this procedure has proven to be effective and results in a reasonable approximation to the solution of the boundary value problem in partial differential equations. For the identification problem, it is shown that the constant parameters are identified to the same accuracy as the supplementary data used in the identification procedure. (Author)