60
Views
7
CrossRef citations to date
0
Altmetric
Section B

A class of explicit two-step superstable methods for second-order linear initial value problems

&
Pages 1424-1432 | Received 15 Jun 2007, Accepted 30 Nov 2007, Published online: 17 Jun 2009

References

  • Chawla , M. M. 1985 . Superstable two-step methods for the numerical integration of general second order initial value problems . J. Comput. Appl. Math. , 12 : 217 – 220 .
  • Coleman , J. P. 2003 . Order conditions for a class of two-step methods for y″=f(x, y) . IMA J. Numer. Anal. , 23 : 197 – 220 .
  • Dahlquist , G. 1978 . On accuracy and unconditional stability of linear multistep methods for second order differential equations . BIT , 18 : 133 – 136 .
  • Gautschi , W. 1961 . Numerical integration of ordinary differential equations based on trignometric polynomials . Numer. Math. , 3 : 381 – 397 .
  • Hairer , E. 1979 . Unconditionally stable methods for second order differential equations . Numer. Math. , 32 : 373 – 379 .
  • Jain , M. K. 1984 . Numerical Solution of Differential Equations , 2 , New Delhi : New Age International (P) Ltd .
  • King , A. C. , Billingham , J. and Otto , S. R. 2003 . Differential Equations , Cambridge University Press .
  • Lambert , J. D. 1973 . Computational Methods in Ordinary Differential Equations , London : John Wiley & Sons .
  • Lambert , J. D. and Watson , I. A. 1976 . Symmetric multistep methods for periodic initial value problems . J. Inst. Math. Appl. , 18 : 189 – 202 .
  • Rai , A. S. and Ananthakrishnaiah , U. 1996 . Additive parameters methods for the numercal integration of . J. Comput. Appl. Math. , 67 : 271 – 276 .
  • Rai , A. S. and Ananthakrishnaiah , U. 1997 . Obrechkoff methods having additional parameters for general second order differential equations . J. Comput. Appl. Math. , 79 : 167 – 182 .
  • Saldanha , G. 2003 . Single cell discretization of order two and four for self-adjoint elliptic equations . Appl. Math. Comput. , 134 : 1 – 8 .
  • Saldanha , G. 2007 . Single cell high order difference schemes for Poisson's equation in three variables . Appl. Math. Comput. , 186 : 548 – 557 .
  • Saldanha , G. and Ananthakrishnaiah , U. 1995 . A fourth-order finite difference scheme for two-dimensional nonlinear elliptic partial differential equations . Numer. Meth. Partial Differ. Equ. , 11 : 33 – 40 .
  • Saldanha , G. and Achar , Sujatha D. 2006 . Symmetric multistep methods with zero phase-lag for periodic initial value problems of second order differential equations . Appl. Math. Comput. , 175 : 401 – 412 .
  • Simos , T. E. , Famelis , I. T. and Tsitouras , Ch. 2003 . Zero dissipative, explicit Numerov-type methods for second order IVPs with oscillating solutions . Numer. Algorithms , 34 : 27 – 40 .
  • Tsitouras , Ch. and Simos , T. E. 1998 . Explicit high order methods for the numerical integration of periodic initial value problems . Appl. Math. Comput. , 95 : 15 – 26 .

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.