Application of sinc-collocation method for solving an inverse problem (Q732163)

The authors consider the inverse problem of determining functions \(u\) and \(p\) satisfying the parabolic equation \(u_t= u_{xx}+ p(t)u+ q(x,t)\), \(0 < x < 1\), \(0<t<T\), with given initial-boundary conditions and an overspecified energy condition of the form \(\int_0^1 u(x,t)\,dx= E(t)\), \(0\leq t\leq T\), where \(q\) and \(E\) are given functions. This problem is transformed into a system of three Volterra integral equations for three unknown time-dependent functions. For the approximate solution of this system of Volterra equations, a sinc-collocation method is considered. It is shown that under some analyticity conditions on the given functions, the maximum norm errors decay exponentially in terms of the size of the sinc base system. Finally some numerical results are presented.