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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 un(x, t) converges to the exact solution u(x, t). Moreover, the partial derivatives of un(x, t) are also convergent to the partial derivatives of u(x, t). And the approximate sequence un(x, t) is the best approximation under a complete normal orthogonal system. [ABSTRACT FROM AUTHOR]