Numerical Method for the Inverse Boundary-Value Problem of the Heat Equation

Resumo

The article considers the inverse boundary-value problem of heat conduction which involves determining the time distribution of temperature on the boundary given the spatial distribution of the temperature at the final time instant. The problem is reduced to an integral equation of the first kind with a symmetrical kernel. The integral equation is solved by a special iterative method. Test examples demonstrate convergence and stability of the proposed method.