14
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

A sixth order method for the integration of two point boundary value problems

Pages 349-360 | Published online: 21 Dec 2010

References

  • Aziz , A.K. and Hubbard , B.E. 1964 . Bounds for the Solution of the Sturm-Liouville Problem with Application to Finite Difference Methods . J. SIAM , 12 : 163 – 168 .
  • Bramble , J.H. and Hubbard , B.E. 1962 . On a Finite Difference Analogue of an Elliptic Boundary Value Problem which is neither Diagonally Dominant nor of Non-negative Type . J. Math. and Phys. , 43 : 117 – 132 .
  • Brown , R.R. 1962 . Numerical Solution of Boundary Value Problems using Non-Uniform Grids . J. SIAM , 10 : 475 – 495 .
  • Faddeeva , V.N. 1958 . Computational Methods of Linear Algebra Dover , New York
  • Fischer , C.F. and Usmani , R.A. 1969 . Properties of Some Tridiagonal Matrices and their Application to Boundary Value Problems . SIAM J. Numer. Anal. , 6 : 127 – 142 .
  • Fox , L. 1957 . The Numerical Solution of Two Point Boundary Value Problems in Ordinary Differential Equations , Oxford University Press .
  • Henrici , P. 1961 . Discrete Variable Methods in Ordinary Differential Equations , New York : John Wiley .
  • Milne , W.E. 1960 . Numerical Solution of Differential Equations , New York : John Wiley .
  • Ridley , C.E. 1956 . A Numerical Method of Solving Second Order Linear Differential Equations with Two Point Boundary Conditions . Proc. Cambridge Phil. Soc. , 53 : 442 – 447 .
  • Roberts , S.M. and Shipman , J.S. 1972 . Two-Point Boundary Value Problems: Shooting Methods , New York : American Elsevier .
  • Rutherford , D.E. 1952 . Some Continuant Determinants arising in Physics and Chemistry II . Proc. Roy. Soc. Edinburgh A , A63 : 232 – 241 .
  • Urabe , M. 1970 . An Implicit One-Step Method of High-Order Accuracy for the Numerical Integration of Ordinary Differential Equations . Numer. Math. , 15 : 151 – 164 .
  • Usmani , R.A. 1972 . A Multi-Step Method for the Numerical Integration of Ordinary Integration of Ordinary Differential Equations . ZAMP , 23 : 465 – 483 .
  • Usmani , R.A. 1971 . Properties of a Five-Band Matrix and its Application to Boundary Value Problem . J.Linear Algebra and Its Applications , 4 : 101 – 115 .
  • Usmani , R.A. 1972 . Minimum Error Bounds for Boundary Value Problems . Proceedings of Canadian Mathematical Congress . June 16-18 1972 . pp. 585 – 594 .
  • Usmani , R.A. 1971 . An O(h6) Finite Difference Analogue for the Numerical Solution of a Two Point Boundary Value Problems . J. Inst. Maths. Applics , 8 June : 335 – 343 .
  • Varga , R.S. 1962 . Matrix Iterative Analysis , NJ : Prentice Hall .
  • Varga , R.S. 1965 . Iterative Methods for Solving Matrix Equations . American Math, Monthly , 72 ( 2 ) February Part II, Computers and Computing

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.