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Approximate solutions for mixed boundary value problems by finite-difference methods


Author: V. Thuraisamy
Journal: Math. Comp. 23 (1969), 373-386
MSC: Primary 65.66
DOI: https://doi.org/10.1090/S0025-5718-1969-0242390-X
MathSciNet review: 0242390
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Abstract: For mixed boundary value problems of Poisson and/or Laplace's equations in regions of the Euclidean space $ {E_n}$, $ n \geqq 2$, finite-difference analogues are formulated such that the matrix of the resulting system is of positive type. Discretization errors are established in a manner to reveal the continuous dependence of the rate of convergence on the smoothness of the solution. Isolated data singularities and their application to exterior problems are also discussed.


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DOI: https://doi.org/10.1090/S0025-5718-1969-0242390-X
Article copyright: © Copyright 1969 American Mathematical Society