Convergence rates of 𝐴𝐷𝐼 methods with smooth initial error

Convergence rates of $\textrm {ADI}$ methods with smooth initial error
HTML articles powered by AMS MathViewer

by Robert E. Lynch and John R. Rice PDF

Math. Comp. 22 (1968), 311-335 Request permission

References

N. I. Achieser, Theory of approximation, Frederick Ungar Publishing Co., New York, 1956. Translated by Charles J. Hyman. MR 0095369
Garrett Birkhoff, Richard S. Varga, and David Young, Alternating direction implicit methods, Advances in Computers, Vol. 3, Academic Press, New York, 1962, pp. 189–273. MR 0168131

J. Soc. Indust. Appl. Math.

28

Willis H. Guilinger Jr., The Peaceman-Rachford method for small mesh increments, J. Math. Anal. Appl. 11 (1965), 261–277. MR 183125, DOI 10.1016/0022-247X(65)90086-7
R. E. Lynch, J. R. Rice, and D. H. Thomas, Tensor product analysis of partial difference equations, Bull. Amer. Math. Soc. 70 (1964), 378–384. MR 169390, DOI 10.1090/S0002-9904-1964-11105-8
Robert E. Lynch, John R. Rice, and Donald H. Thomas, Direct solution of partial difference equations by tensor product methods, Numer. Math. 6 (1964), 185–199. MR 213047, DOI 10.1007/BF01386067
Robert E. Lynch, John R. Rice, and Donald H. Thomas, Tensor product analysis of alternating direction implicit methods, J. Soc. Indust. Appl. Math. 13 (1965), 995–1006. MR 198699, DOI 10.1137/0113067
D. W. Peaceman and H. H. Rachford Jr., The numerical solution of parabolic and elliptic differential equations, J. Soc. Indust. Appl. Math. 3 (1955), 28–41. MR 71874, DOI 10.1137/0103003

The Approximation of Functions

Dunham Jackson, The theory of approximation, American Mathematical Society Colloquium Publications, vol. 11, American Mathematical Society, Providence, RI, 1994. Reprint of the 1930 original. MR 1451140
Antoni Zygmund, Trigonometrical series, Dover Publications, New York, 1955. MR 0072976
Carl de Boor, Bicubic spline interpolation, J. Math. and Phys. 41 (1962), 212–218. MR 158512, DOI 10.1002/sapm1962411212