Abstract
This paper develops an iterative algorithm for the solution to a variable-coefficient semilinear heat equation with nonlocal boundary conditions in the reproducing space. It is proved that the approximate sequence u n (x, t) converges to the exact solution u(x, t). Moreover, the partial derivatives of u n (x, t) are also convergent to the partial derivatives of u(x, t). And the approximate sequence u n (x, t) is the best approximation under a complete normal orthogonal system.