parameter determination in a parabolic inverse problem in general dimensions

it is well known that the parabolic partial differential equationsin two or more space dimensions with overspecified boundary data,feature in the mathematical modeling of many phenomena. in thisarticle, an inverse problem of determining an unknowntime-dependent source term of a parabolic equation in generaldimensions is considered. employing some transformations, wechange the inverse problem to a volterra integral equation ofconvolution-type. by using an explicit procedure based on sincfunction properties, the resulting integral equation is replacedby a system of linear algebraic equations. the convergenceanalysis is included, and it is shown that the error in theapproximate solution is bounded in the infinity norm by thecondition number and the norm of the inverse of the coefficientmatrix multiplied by a factor that decays exponentially with thesize of the system. some numerical examples are given todemonstrate the computational efficiency of the method.