  We provide an accurate verification method for solutions of heat equations
with a superlinear nonlinearity. The verification method numerically proves the
existence and local uniqueness of the exact solution in a neighborhood of a
numerically computed approximate solution. Our method is based on a fixed-point
formulation using the evolution operator, an iterative numerical verification
scheme to extend a time interval in which the validity of the solution can be
verified, and rearranged error estimates for avoiding the propagation of an
overestimate. As a result, compared with the previous verification method using
the analytic semigroup, our method can enclose the solution for a longer time.
Some numerical examples are presented to illustrate the efficiency of our
verification method.
