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https://doi.org/10.1007/s10891-017-1576-z
The Boundary Function Method. Fundamentals
partial differential equations
Robin boundary conditions
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problem
fundamentals
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2021-11-01T18:31
form
differential operators
articles
boundary functions
https://scigraph.springernature.com/explorer/license/
sequence
366-391
The boundary function method is proposed for solving applied problems of mathematical physics in the region defined by a partial differential equation of the general form involving constant or variable coefficients with a Dirichlet, Neumann, or Robin boundary condition. In this method, the desired function is defined by a power polynomial, and a boundary function represented in the form of the desired function or its derivative at one of the boundary points is introduced. Different sequences of boundary equations have been set up with the use of differential operators. Systems of linear algebraic equations constructed on the basis of these sequences allow one to determine the coefficients of a power polynomial. Constitutive equations have been derived for initial boundary-value problems of all the main types. With these equations, an initial boundary-value problem is transformed into the Cauchy problem for the boundary function. The determination of the boundary function by its derivative with respect to the time coordinate completes the solution of the problem.
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2017-03
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2017-03-01
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dimensions_id
pub.1085106214
Pure Mathematics
A. V. Luikov Heat and Mass Transfer Institute, National Academy of Sciences of Belarus, 15 P. Brovka Str., 220072, Minsk, Belarus
A. V. Luikov Heat and Mass Transfer Institute, National Academy of Sciences of Belarus, 15 P. Brovka Str., 220072, Minsk, Belarus
Mathematical Sciences
Numerical and Computational Mathematics
2
V. A.
Kot
Journal of Engineering Physics and Thermophysics
1062-0125
1573-871X
Springer Nature
90
doi
10.1007/s10891-017-1576-z
Springer Nature - SN SciGraph project