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| Paper IPM / M / 7375 |
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| Abstract: | |
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In this paper a two-dimensional heat equation is considered. The
problem has both Numann and Dirichlet boundary conditions and one
non-local condition in which an integral of the unknown solution
u occurs. The Dirichlet boundary condition contains an
additional unknown function μ(t). In this paper the numerical
solution of this equation is treated. Due to the structure of the
boundary conditions a reduced one-dimensional heat equation for
the new unknown v(y,t)=∫u(x,y,t)dx can be formulated. The
resulting problem has a non-local boundary condition. This
one-dimensional heat equation is solved by Saulyev's formula. From
the solution of this one-dimensional problem an approximation of
the function μ(t) is obtained. Once this approximation is
known, the given two-dimensional problem reduces to a standard
heat equation with the usual Neumann's boundary conditions. This
equation is solved by an extension of the Saulyev's techniques.
Results of numerical experiments are presented.
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