Numerical solution of the Neumann boundary value problem for an infinite convolutional system of elliptic equation via the boundary elements method
Journal Title: Дослідження в математиці і механіці - Year 2017, Vol 22, Issue 1
Abstract
We consider a Neumann boundary value problem for an infinite convolutional system of elliptic equations obtained as a result of the application of the Laguerre transform in the time domain to initial-boundary value problems for evolution equations in 3d Lipschitz domains. With help of q-convolution of sequences the integral representation of the generalized solution of the problem is built and an equivalent system of boundary integral equations is obtained. The existence and uniqueness of the numerical solution obtained by the boundary elements method are proven. A priory error estimates are investigated. Numerical results obtained for the modal problems are given.
Authors and Affiliations
Yu. A. Muzychuk
Keywords
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