Approximate solution for a variable-coefficient semilinear heat equation with nonlocal boundary conditions

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.

Keywords:

• approximate solution
• nonlinear parabolic equation
• reproducing kernel space
• nonlocal boundary condition

2000 AMS Subject Classifications :

• 35K55
• 35K58
• 35K10
• 35K20