A GLOBAL TIME TREATMENT FOR INVERSE HEAT-CONDUCTION PROBLEMS

A new global time treatment is proposed and demonstrated for inverse h ear conduction problems. This exposition illustrates the methodology b y carefully and meticulously investigating the classic Beck's problem. It is shown that accurate and stable numerical results occur without resorting to any stabilizing scheme beyond the implementation of a glo bal basis representation for the temperature distribution. As a global time method the entire space-time domain is resolved in a simultaneou s fashion. The approach is also extendable to multidimensional and mul tiprobe situations without difficulty. In direct problems the method h as been successively applied to initial value problems, Volterra integ ral equations, and parabolic and hyperbolic partial and integro-partia l differential equations.