Monotone type discrete analogue for the mixed boundary value problem.
Abstract: This paper is concerned with the formulation of finite-difference analogues of mixed boundary value problems for Poisson's equation. A discrete approximation to the normal derivative is devised such that the matrix of the resulting system is of monotone type. This enables us to prove that the rate of convergence is , where h is the mesh constant.
-  James H. Bramble and Bert E. Hubbard, New monotone type approximations for elliptic problems, Math. Comp. 18 (1964), 349–367. MR 0165702, https://doi.org/10.1090/S0025-5718-1964-0165702-X
-  J. H. Bramble and B. E. Hubbard, Approximation of solutions of mixed boundary value problems for Poisson’s equation by finite differences, J. Assoc. Comput. Mach. 12 (1965), 114–123. MR 0171384, https://doi.org/10.1145/321250.321260
-  V. Thuraisamy, Approximate solutions for mixed boundary value problems by finite-difference methods, Math. Comp. 23 (1969), 373–386. MR 0242390, https://doi.org/10.1090/S0025-5718-1969-0242390-X
-  Richard S. Varga, Matrix iterative analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0158502
- J. H. Bramble & B. E. Hubbard, ``New monotone type approximations for elliptic problems,'' Math. Comp., v. 18, 1964, pp. 349-367. MR 29 #2982. MR 0165702 (29:2982)
- J. H. Bramble & B. E. Hubbard, ``Approximation of solutions of mixed boundary value problems for Poisson's equation by finite differences,'' J. Assoc. Comput. Mach., v. 12, 1965, pp. 114-123. MR 30 #1615. MR 0171384 (30:1615)
- V. Thuraisamy, ``Approximate solutions for mixed boundary value problems by finitedifference methods,'' Math. Comp., v. 23, 1969, pp. 373-386. MR 0242390 (39:3721)
- R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood, Cliffs, N. J., 1962. MR 28 #1725. MR 0158502 (28:1725)
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