Approximation of Solutions of Mixed Boundary Value Problems for Poisson's Equation by Finite Differences

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Approximation of Solutions of Mixed Boundary Value Problems for Poisson's Equation by Finite Differences

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Journal of the ACM (JACM) archive
Volume 12 , Issue 1 (January 1965) table of contents

Pages: 114 - 123

Year of Publication: 1965

ISSN:0004-5411

Authors

J. H. Bramble	Institute for Fluid Dynamics & Applied Mathematics, The University of Maryland, College Park, Maryland
B. E. Hubbard	Institute for Fluid Dynamics & Applied Mathematics, The University of Maryland, College Park, Maryland

Publisher

ACM New York, NY, USA

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	ALEN, D. N. DEG. Relaxation Methods. McGraw-Hill, New York, 1954.
	2	BATSCHELET. Ober die numerische AnflSsung von Randwertproblemen bei ellipti schen particllea Differentialgleichungen. Z. Angew. Math. Phys. 3, 1952.
	3	BRAMBLe, J.H. Fourth order finite-difference analogues of the Dirichlet problem for Poisson's equation in three trod four dimensions. Math. Comput. 17 (1963), 217-222.
	4	BRAMIBLE, J- H. AND 'BBARD, B. E. Oil the formulation of finite-difference analogues of the Dirichlet problem for Poisson's equation. Numer. Math. 4 (1962), 313-327.
	5	---- aND --. A theorem on error estimation for finite-difference analogues of the Dirichlet problem for elliptic equations. Contrib. Diff. Eq. 2 (1963), 319-340.
	6	---- AND .... - A priori bounds on the discretization error in the numerical solution of the Dirichlet problem. Contrib. Diff. Eq. 2 (1963), 229-252.
	7	--- AND -----. On a finite-diference analogue of an elliptic boundary problem which is neither diagonally dominant nor of non-negative type. J. Math. Phys. 43 (1964), 117-135.
	8	F0SYTHE, G., AND WASOW, W. Finite Diffrcnce Methods for Partial Differential Equations. Wiley, New York, 1960.
	9	GERSCIIGORN, S. Fehlerabschgtzung f0tr das Differenzenverfahren zur Losung Partiel- Ier Differentidgle.iehungcn. Z. Angew. MW.h. Mech. 10 (19}0), 373-352.
	10	garsea, D. On the Numerical Solution of Problems Allowing Mixed Boundary Conditions. Notices Am. Math. Soc. IO (1963), 92.
	11	KroovfL L. ND KRYLOV, V. Approximate Melhd. of Higher" Analysis. Noordhog Lgd., Netherlands, I958.
	12	SHORTLE, G. ANd YELLI,II-, R, The numerical solution of Laplnee's equation. j. Appt. Phys. 9 (1938), 334.-348.
	13	SHAW, F.S. An rtrodaction o Relaxation Methods. Dowr, New York, 1950,
	14	SYNGE, J. L. ANO SctuHIULD A. Tensor Calculus. U. of Toront, oF Press, Toronto, 1952.
	15	UmLMAN. Differenzenverhhren fur die 2. und 3. Randwerufgabe mit Rfitderu bei ?u(z, y) = r(X, y, u). g. Anoew. Math. Mech. 38 (1958).
	16	VISWANATHAN R.. V. Sohdon of Poisson's equation by relaxation method-normal gradient specified or curved boundaries, Math. Tabcs Aids Cotipg, 11 (1957).