381
Views
3
CrossRef citations to date
0
Altmetric
Section B

Higher order time integration formula with application on Burgers’ equation

&
Pages 756-771 | Received 10 Jun 2013, Accepted 24 Mar 2014, Published online: 22 May 2014

References

  • T.D. Bui, Some A-stable and L-stable methods for the numerical integration of stiff ordinary differential equations, J. Assoc. Comput. Mach. 26(3) (1979), pp. 483–493. doi: 10.1145/322139.322147
  • M.M. Chawla and M.A. Al-Zanaidi, New L-stable modified trapezoidal formulas for the numerical integration of y′=f (x, y), Int. J. Comput. Math. 63 (1997), pp. 279–288. doi: 10.1080/00207169708804567
  • M.M. Chawla and D.J. Evans, A new L-stable Simpson type rule for the diffusion equation, Int. J. Comput. Math. 82 (2005), pp. 601–607. doi: 10.1080/00207160512331331138
  • M.M. Chawla, M.A. Al-Zanaidi, and M.S. Al-Sahhar, Stabilized fourth order extended methods for the numerical solution of ODEs, Int. J. Comput. Math. 52 (1994), pp. 99–107. doi: 10.1080/00207169408804294
  • J.D. Cole, On a quasilinear parabolic equation occurring in aerodynamics, Q. Appl. Math. 9 (1951), pp. 225–236.
  • J. Crank and P. Nicolson, A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type, Proc. Cambridge Philos. Soc. 43 (1947), pp. 50–67. doi: 10.1017/S0305004100023197
  • G. Dahlquist, A special stability problem for linear multistep methods, BIT 3 (1963), pp. 27–43. doi: 10.1007/BF01963532
  • E. Hopf, The partial differential equation , Commun. Pure Appl. Math. 3 (1950), pp. 201–230. doi: 10.1002/cpa.3160030302
  • M. Inc, New L-stable method for numerical solutions of ordinary differential equations, Appl. Math. Comput. 188 (2007), pp. 779–785. doi: 10.1016/j.amc.2006.10.055
  • M.K. Kadalbajoo and A. Awasthi, A numerical method based on Crank–Nicolson scheme for Burgers’ equation, Appl. Math. Comput. 182 (2006), pp. 1430–1442. doi: 10.1016/j.amc.2006.05.030
  • J.D. Lambert, Numerical Methods for Ordinary Differential Systems, John Wiley, New York, 1991.
  • J.D. Lawson and J.L. Morris, The extrapolation of first order methods for parabolic partial differential equations I, SIAM J. Numer. Anal. 15 (1978), pp. 1212–1224. doi: 10.1137/0715082
  • R.J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM, Philadelphia, 2007.
  • K. Pandey, L. Verma, and A.K. Verma, L-stable Simpson's 3/8 rule and Burgers’ equation, Appl. Math. Comput. 218 (2011), pp. 1342–1352. doi: 10.1016/j.amc.2011.06.017
  • R.D. Richtmyer and K.W. Morton, Difference Methods for Initial-Value Problems, Wiley-Interscience, New York, 1967.
  • G.D. Smith, Numerical Solution of Partial Differential Equations, Oxford University Press, Oxford, 1978.
  • L. Verma, L-stable derivative-free error-corrected trapezoidal rule for Burgers’ equation with inconsistent initial and boundary conditions, Int. J. Math. Math. Sci. 2012 (2012), Article ID 821907, 13 pages.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.