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

Thuraisamy, V.

doi:10.1090/S0025-5718-1969-0242390-X

Approximate solutions for mixed boundary value problems by finite-difference methods
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Math. Comp. 23 (1969), 373-386 Request permission

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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