Bibliography for the Crank-Nicolson Method for PDE's

short

Remark.  A common misspelling is Nicholson.

  1. The alternating segment Crank-Nicolson method for solving convection-diffusion equation with variable coefficient.  
    Wang, Wen Qia
    Appl. Math. Mech. (English Ed.)  24  (2003),  no. 1, 32--42;  translated from  Appl. Math. Mech.  24  (2003),  no. 1, 29--38(Chinese), MathSciNet.  
  2. Sharpening the estimate of the stability constant in the maximum-norm of the Crank-Nicolson scheme for the one-dimensional heat equation
    Farago, I.; Palencia, C.
    Applied Numerical Mathematics, v 42, n 1-3, August, 2002, p 133-140, Compendex.
  3. Crank-Nicolson finite difference method for two-dimensional diffusion with an integral condition
    Dehghan, M.
    Applied Mathematics and Computation (New York), v 124, n 1, Nov 10, 2001, p 17-27, Compendex.
  4. A Crank-Nicolson orthogonal spline collocation method for vibration problems.
    Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard
    Proceedings of the Fourth International Conference on Spectral and High Order Methods (ICOSAHOM 1998) (Herzliya). Appl. Numer. Math. 33 (2000), no. 1-4, 299--306, MathSciNet.  
  5. Crank-Nicolson-Galerkin model for transport in groundwater: refined criteria for accuracy.
    Hossain, Md. Akram; Miah, A. S.
    Appl. Math. Comput. 105 (1999), no. 2-3, 173--181, MathSciNet.  
  6. Alternating Crank-Nicolson method for decoupling the Ginzburg-Landau equations
    Mu, Mo; Huang, Yunqing
    SIAM Journal on Numerical Analysis, v 35, n 5, Oct, 1998, p 1740-1761, Compendex.
  7. Linearized Crank-Nicolson-Galerkin method for the Ginzburg-Landau model
    Mu, Mo
    SIAM Journal on Scientific Computing, v 18, n 4, Jul, 1997, p 1028-1039, Compendex.
  8. New crank-nicholson algorithm for solving the diffusive wave flood routing equation along a complex channel network
    Moussa, R.; Bouquillon, C.
    Proc 7 Int Conf Comput Methods Exp Meas CMEM 95, 1995, p 221, Compendex.
  9. Alternating block crank-nicolson method for the 3-D heat equation
    Jing, Chen
    Applied Mathematics and Computation (New York), v 66, n 1, Nov, 1994, p 41--61, Compendex.
  10. Alternating band Crank-Nicolson method for  u t = u xx + u yy.
    Chen, Jing; Zhang, Bao Lin
    A Chinese summary appears in Gaoxiao Yingyong Xuebao Ser. A  8 (1993), no. 4, 451.  Gaoxiao Yingyong Shuxue Xuebao Ser. B  8  (1993),  no. 2, 150--162, MathSciNet.  
  11. Unconditional Convergence of Some Crank-Nicolson Lod Methods for Initial- Boundary Value Problems
    Willem Hundsdorfer
    Mathematics of Computation, Vol. 58, No. 197. (Jan., 1992), pp. 35-53, Jstor.  
  12. A Crank-Nicolson scheme for Hodgkin-Huxley equations. (Spanish)
    López Marcos, J. C.
    Proceedings of the XII Congress on Differential Equations and Applications/II Congress on Applied Mathematics (Spanish) (Oviedo, 1991), 497--502, Univ. Oviedo, Oviedo, 1991, MathSciNet.  
  13. Stability and asymptotic behavior of a numerical solution corresponding to a diffusion-reaction equation solved by a finite difference scheme (Crank-Nicolson)
    Cherruault, Y.; Choubane, M.; Valleton, J.M.; Vincent, J.C.
    Computers & Mathematics with Applications, v 20, n 11, 1990, p 37-46, Compendex.
  14. A comparison of the Crank-Nicolson and waveform relaxation multigrid methods on the Intel hypercube.
    Vandewalle, Stefan; Piessens, Robert
    Proceedings of the Fourth Copper Mountain Conference on Multigrid Methods (Copper Mountain, CO, 1989), 417--434, SIAM, Philadelphia, PA, 1989, MathSciNet.  
  15. Crank-Nicolson-Galerkin approximation of the periodic solutions of weakly nonlinear parabolic equations.
    Olejniczak, A.
    Zastos. Mat. 18 (1985), no. 4, 663--680, MathSciNet.  
  16. Two New Finite Difference Schemes for Parabolic Equations  
    J. R. Cash  
    SIAM Journal on Numerical Analysis, Vol. 21, No. 3. (Jun., 1984), pp. 433-446, Jstor.  
  17. An exceptional case to the Crank-Nicolson method.
    Whittaker, James V.
    Appl. Math. Notes 8 (1983), no. 3-4, 27--32, MathSciNet.  
  18. On the smoothing property of the Crank-Nicolson scheme.
    Luskin, Mitchell; Rannacher, Rolf
    Applicable Anal. 14 (1982/83), no. 2, 117--135, MathSciNet.  
  19. Linear combinations of generalized Crank-Nicolson schemes.  
    Gourlay, A. R.; Morris, J. Ll.
    IMA J. Numer. Anal.  1  (1981), no. 3, 347--357, MathSciNet.  
  20. Stability and Convergence of a Generalized Crank-Nicolson Scheme on a Variable Mesh for the Heat Equation
    Pierre Jamet
    SIAM Journal on Numerical Analysis, Vol. 17, No. 4. (Aug., 1980), pp. 530-539, Jstor.  
  21. Stability Restrictions on Second Order, Three Level Finite Difference Schemes for Parabolic Equations  
    J. M. Varah  
    SIAM Journal on Numerical Analysis, Vol. 17, No. 2. (Apr., 1980), pp. 300-309, Jstor.  
  22. A Crank-Nicolson-H^-1-Galerkin Procedure for Parabolic Problems in a Single-Space Variable
    Richard P. Kendall, Mary F. Wheeler
    SIAM Journal on Numerical Analysis, Vol. 13, No. 6. (Dec., 1976), pp. 861-876, Jstor.  
  23. Numerical solution of parabolic problems by the generalized Crank-Nicolson scheme.
    Nassif, Nabil R.
    Calcolo 12 (1975), no. 1, 51--61, MathSciNet.  
  24. On the Instability of Leap-Frog and Crank-Nicolson Approximations of a Nonlinear Partial Differential Equation
    B. Fornberg
    Mathematics of Computation, Vol. 27, No. 121. (Jan., 1973), pp. 45-57, Jstor.  
  25. Convergent Finite Difference Schemes for Nonlinear Parabolic Equations  
    Albert C. Reynolds, Jr.  
    SIAM Journal on Numerical Analysis, Vol. 9, No. 4. (Dec., 1972), pp. 523-533, Jstor.  
  26. A comparison of Crank-Nicolson and Chebyshev rational methods for numerically solving linear parabolic equations.
    Cavendish, J. C.; Culham, W. E.; Varga, R. S.
    J. Computational Phys. 10 (1972), 354--368, MathSciNet.  
  27. A high-order Crank-Nicholson technique for solving differential equations.
    Davison, E. J.
    Comput. J. 10 1967 195--197, MathSciNet.  
  28. On the instability of the Crank Nicholson formula under derivative boundary conditions.
    Keast, P.; Mitchell, A. R.
    Comput. J. 9 1966 110--114, MathSciNet.  
  29. An extrapolated Crank-Nicolson difference scheme for quasilinear parabolic equations.
    Lees, Milton
    1967 Nonlinear Partial Differential Equations: A Symposium on Methods of Solution (Newark, Del., 1965) pp. 193--201 Academic Press, New York, MathSciNet.  
  30. On the order of convergence of the Crank-Nicolson procedure.
    Strang, Gilbert
    J. Math. Phys. 38 1959/1960 141--144, MathSciNet.  
  31. On the Crank-Nicolson procedure for solving parabolic partial differential equations.
    Juncosa, M. L.; Young, David
    Proc. Cambridge Philos. Soc. 53 (1957), 448--461, MathSciNet.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004