Approximations for a Cauchy problem for the heat equation
- 1 May 1987
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 3 (2) , 263-273
- https://doi.org/10.1088/0266-5611/3/2/009
Abstract
A Cauchy problem for the heat equation in the quarter plane is considered. Data are given along the line x=1 and the solution at x=0 is sought. The problem is ill-posed: the solution does not depend continuously on the data. In order to solve the problem numerically it is necessary to modify the equation so that a bound on the solution is imposed (explicitly or implicitly). The author studies a modification of the equation, where a fourth-order mixed derivative term is added. Error estimates for this equation are given, which show that the solution of the modified equation is an approximation of the solution of the Cauchy problem for the heat-equation.Keywords
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