scholarly journals Boundary control for the heat equation with non-linear boundary condition

1989 ◽  
Vol 78 (1) ◽  
pp. 89-121 ◽  
Author(s):  
E.J.P.Georg Schmidt
Keyword(s):  
Boundary Condition ◽  
Heat Equation ◽  
Boundary Control ◽  
Linear Boundary ◽  
Linear Boundary Condition ◽  
Non Linear

Polynomial approximations to the solution of the heat equation

1973 ◽  
Vol 73 (1) ◽  
pp. 157-165 ◽  
Author(s):  
R. E. Scraton
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Partial Differential Equation ◽  
Exact Solution ◽  
Heat Equation ◽  
Least Squares ◽  
Linear Boundary ◽  
Chebyshev Series ◽  
Linear Boundary Condition ◽  
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AbstractAn approximation is found to the solution of the partial differential equationin the region −1 ≤ x ≤ 1, t > 0, where u satisfies a general linear boundary condition on x = ± 1. This approximation is a polynomial in x, and is an exact solution of a perturbed form of the differential equation. By choosing the perturbation appropriately, this approach is mathematically equivalent to some recent methods for solving the differential equation in the form of a Chebyshev series. Better approximations to the required solution (and particularly to the eigenvalues) are obtained by choosing the perturbation to satisfy a least squares criterion.

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