Numerical Approximation of a Cauchy Problem for a Parabolic Partial Differential Equation.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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In many physical problems in heat conduction, it is impossible to obtain an initial temperature distribution within a material. In many of these cases, in order to obtain approximations of the temperature within the body, one must rely entirely upon data which can be measured at the boundary. An additional problem is that these boundary data are only accurate to within some prescribed measurement errors. The purpose of this paper is to define a procedure for numerically approximating the solution of one such heat flow problem and to present explicit error estimates for the numerical procedure. A priori error estimates are presented when the data are known only approximately.
- Numerical Mathematics