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Method of Refinement by Higher Order Differences for 3D Poisson Equation with Nonlocal Boundary Conditions |
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PP: 71-77 |
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doi:10.18576/msl/070201
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Author(s) |
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Givi Berikelashvili,
Murli M. Gupta,
Bidzina Midodashvili,
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Abstract |
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| We consider the Bitsadze−Samarskii type nonlocal boundary value problem for Poisson equation in a unit cube, which is
first solved by a difference scheme of second-order accuracy. Using this approximate solution, we correct the right-hand side of the
difference scheme. It is shown that the solution of the corrected scheme converges at the rate O(hs) in the discrete L2-norm provided
that the exact solution of the original problem belongs to the Sobolev space with exponent s ∈ [2,4]. |
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