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Approximate solution for a variable-coefficient semilinear heat equation with nonlocal boundary conditions. (English) Zbl 1182.35143
Summary: 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.

MSC:
35K58 Semilinear parabolic equations
35A35 Theoretical approximation in context of PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
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