The numerical solution of partial differential equations
Author:
Howard W. Emmons
Journal:
Quart. Appl. Math. 2 (1944), 173-195
MSC:
Primary 65.0X
DOI:
https://doi.org/10.1090/qam/10680
MathSciNet review:
10680
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Additional Information
- Mark Kormes, Numerical solution of the boundary value problem for the potential equation by means of punched cards, Rev. Sci. Instruments 14 (1943), 248–250. MR 9161
H. Liebmann, Die angenäherte Ermittlung harmonischer Funktionen und konformer Abbildungen, Sitzungsber. Münchener Akad., 1918, 385.
F. Wolf, Über die angenäherte numerische Berechnung harmonischer und biharmonischer Funktionen, Z. angew. Math. u. Mech., 6, 118—150 (1926).
R. Courant, Über Randwertaufgaben bei partiellen Differenzengleichungen, Z. angew. Math. u. Mech., 6, 322—325 (1926).
A. Thom, The flow past circular cylinders at low speeds, Proc. Roy. Soc. London, A, 141, 651—669 (1933).
G. Shortley and R. Weller, The numerical solution of Laplace’s equation, J. Appl. Phys., 9, 334—348 (1938).
R. Von Mises and H. Geiringer, Praktische Verfahren der Gleichungsauflösung, Z. angew. Math u. Mech., 9, 58—76, 152—164 (1929).
- 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, DOI https://doi.org/10.1007/BF01448839
D. G. Christopherson and R. V. Southwell, Relaxation methods applied to engineering problems. III. Problems involving two independent variables, Proc. Roy. Soc. London, A, 168, 317—350 (1938).
- Richard V. Southwell, New pathways in aeronautical theory, J. Aeronaut. Sci. 9 (1942), 77–87; discussion, 87–89. MR 5855
S. Timoshenko, Theory of plates and shells, McGraw-Hill Book Co., 1st ed., 1940, p. 187.
- R. V. Southwell, Relaxation Methods in Engineering Science. A treatise on approximate computation, Oxford Engineering Science Series, Oxford University Press, New York, 1940. MR 0005425
- Derman G. Christopherson, A new mathematical method for the solution of film lubrication problems, Inst. Mech. Engrs. J. Proc. 146 (1941), 126–135. MR 0006295
H. Bateman, Partial differential equations, Cambridge Univ. Press, 1932, pp. 169—171.
M. Kormes, Numerical solution of the boundary value problem for the potential equation by means of punched cards, Rev. Sci. Instruments, 14 (1943).
H. Liebmann, Die angenäherte Ermittlung harmonischer Funktionen und konformer Abbildungen, Sitzungsber. Münchener Akad., 1918, 385.
F. Wolf, Über die angenäherte numerische Berechnung harmonischer und biharmonischer Funktionen, Z. angew. Math. u. Mech., 6, 118—150 (1926).
R. Courant, Über Randwertaufgaben bei partiellen Differenzengleichungen, Z. angew. Math. u. Mech., 6, 322—325 (1926).
A. Thom, The flow past circular cylinders at low speeds, Proc. Roy. Soc. London, A, 141, 651—669 (1933).
G. Shortley and R. Weller, The numerical solution of Laplace’s equation, J. Appl. Phys., 9, 334—348 (1938).
R. Von Mises and H. Geiringer, Praktische Verfahren der Gleichungsauflösung, Z. angew. Math u. Mech., 9, 58—76, 152—164 (1929).
R. Courant, K. Friedrichs and H. Lewy, Über die partiellen Differenzengleichungen der mathematischen Physik, Math. Ann., 100, 22—74 (1928).
D. G. Christopherson and R. V. Southwell, Relaxation methods applied to engineering problems. III. Problems involving two independent variables, Proc. Roy. Soc. London, A, 168, 317—350 (1938).
R. V. Southwell, New pathways in aeronautical theory, 5th Wright Brothers Lecture, J. Aer. Sci., 9, 77—89 (1942).
S. Timoshenko, Theory of plates and shells, McGraw-Hill Book Co., 1st ed., 1940, p. 187.
R. V. Southwell, Relaxation methods in engineering science, Oxford Univ. Press, 1940, Chapters VII and VIII.
D. G. Christopherson, A new mathematical method for the solution of film lubrication problems, J. Inst. Mech. Eng., 146, 126—135 (1942).
H. Bateman, Partial differential equations, Cambridge Univ. Press, 1932, pp. 169—171.
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Article copyright:
© Copyright 1944
American Mathematical Society
