• [1] R. Courant, K. Friedrichs, and H. Lewy, Über die partiellen Differenzengleichungen der mathematischen Physik, Math. Ann. 100 (1928), no. 1, 32–74 (German). MR 1512478, http://dx.doi.org/10.1007/BF01448839
• [2] C. W. Cryer, The difference analogue of Gauss’ theorem, SIAM J. Numer. Anal. 4 (1967), 155–162. MR 0213763 (35 #4620)
• [3] C. W. Cryer, "On difference approximations to elliptic partial differential equations in ." (To appear.)
• [4] Dennis Eisen, The equivalence of stability and convergence for finite difference schemes with singular coefficients, Numer. Math. 10 (1967), 20–29. MR 0214295 (35 #5146)
• [5] P. Jamet, Numerical Methods and Existence Theorems for Singular Linear BoundaryValue Problems, Doctoral Thesis, Univ. of Wisconsin, Madison, Wis., 1967.
• [6] Pierre Jamet and Seymour V. Parter, Numerical methods for elliptic differential equations whose coefficients are singular on a portion of the boundary, SIAM J. Numer. Anal. 4 (1967), 131–146. MR 0215543 (35 #6383)
• [7] J. J. Kohn and L. Nirenberg, Degenerate elliptic-parabolic equations of second order, Comm. Pure Appl. Math. 20 (1967), 797–872. MR 0234118 (38 #2437)
• [8] W. V. Koppenfels, Über die Existenz der Lösungen linearer partieller Differentialgleichungen vom elliptischen Typus, Dissertation, Göttingen, 1929.
• [8'] Heinz-Otto Kreiss and Einar Lundqvist, On difference approximations with wrong boundary values, Math. Comp. 22 (1968), 1–12. MR 0228193 (37 #3777), http://dx.doi.org/10.1090/S0025-5718-1968-0228193-X
• [9] Seymour V. Parter, Numerical methods for generalized axially symmetric potentials, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (1965), 500–516. MR 0191113 (32 #8522)
• [9'] Seymour V. Parter, Stability, convergence, and pseudo-stability of finite-difference equations for an over-determined problem, Numer. Math. 4 (1962), 277–292. MR 0148232 (26 #5740)
• [10] P. Raviart, Sur l'Approximation de Certaines Équations d'Évolution Linéaires et Non Linéaires, Doctoral Thesis, Paris, 1965.
• [11] Robert D. Richtmyer, Difference methods for initial-value problems, Interscience tracts in pure and applied mathematics. Iract 4, Interscience Publishers, Inc., New. York, 1957. MR 0093918 (20 #438)
• [12] S. L. Sobolev, Applications of functional analysis in mathematical physics, Translated from the Russian by F. E. Browder. Translations of Mathematical Monographs, Vol. 7, American Mathematical Society, Providence, R.I., 1963. MR 0165337 (29 #2624)

Bibliography

[1]

R. Courant, K. Friedrichs & H. Lewy, "Über die Differenzengleichungen der mathematischen Physik," Math. Ann., v. 100, 1928, pp. 32-74; English transl., New York Univ. Courant Inst. Math. Sci. Res. Dept. N. Y. 0.-7689. MR 1512478

[2]

C. W. Cryer, "The difference analogue of Gauss' theorem," SIAM J. Numer. Anal., v. 4, 1967, pp. 155-162. MR 35 #4620. MR 0213763 (35:4620)

[3]

C. W. Cryer, "On difference approximations to elliptic partial differential equations in ." (To appear.)

[4]

D. Eisen, "The equivalence of stability and convergence for finite difference schemes with singular coefficients," Numer. Math., v. 10, 1967, pp. 20-29. MR 35 #5146. MR 0214295 (35:5146)

[5]

P. Jamet, Numerical Methods and Existence Theorems for Singular Linear BoundaryValue Problems, Doctoral Thesis, Univ. of Wisconsin, Madison, Wis., 1967.

[6]

P. Jamet & S. V. P arter, "Numerical methods for elliptic differential equations whose coefficients are singular on a portion of the boundary," SIAM J. Numer. Anal., v. 4, 1967, pp. 131-146. MR 0215543 (35:6383)

[7]

J. J. Kohn & L. Nirenberg, "Degenerate elliptic-parabolic equations of second order," Comm. Pure Appl. Math., v. 20, 1967, pp. 797-872. MR 0234118 (38:2437)

[8]

W. V. Koppenfels, Über die Existenz der Lösungen linearer partieller Differentialgleichungen vom elliptischen Typus, Dissertation, Göttingen, 1929.

[8']

H. O. Kreiss & E. Lundqvist, "On difference approximations with wrong boundary values," Math. Comp., v. 22, 1968, pp. 1-12. MR 0228193 (37:3777)

[9]

S. V. Parter, "Numerical methods for generalized axially symmetric potentials," J. Soc. Indust. Appl. Math. Ser. B. Numer. Anal., v. 2, 1965, pp. 500-516. MR 32 #8522. MR 0191113 (32:8522)

[9']

S. V. Parter, "Stability, convergence, and pseudo-stability of finite-difference equations for an over-determined problem," Numer. Math., v. 4, 1962, pp. 277-292. MR 26 #5740. MR 0148232 (26:5740)

[10]

P. Raviart, Sur l'Approximation de Certaines Équations d'Évolution Linéaires et Non Linéaires, Doctoral Thesis, Paris, 1965.

[11]

R. D. Richtmyer, Difference Methods for Initial-Value Problems, Interscience, New York, 1957. MR 20 #438. MR 0093918 (20:438)

[12]

S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics, English transl., from Russian transl., Transl. Math. Monographs, vol. 7, Amer. Math. Soc., Providence, R. L, 1963. MR 29 #2624. MR 0165337 (29:2624)