Journal of applied mathematics & informatics

  • 제5권3호
  • /
  • Pages.759-770
  • /
  • 1998
  • /
  • 2734-1194(pISSN)
  • /
  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

CUBIC SPLINE METHOD FOR SOLVING TWO-POINT BOUNDARY-VALUE PROBLEMS

  • Al Said, Eisa-A. (Department of Mathematics king Saud University)
  • 발행 : 1998.09.01

⟨ 이전 논문 다음 논문 ⟩

초록

In this paper we use uniform cubic spline polynomials to derive some new consistency relations. These relations are then used to develop a numerical method for computing smooth approxi-mations to the solution and its first second as well as third derivatives for a second order boundary value problem. The proesent method out-performs other collocations finite-difference and splines methods of the same order. numerical illustratiosn are provided to demonstrate the practical use of our method.

키워드

참고문헌

  1. Math. of Comput. v.29 A collocation method for two-point boundary value problems J.H.Ahlberg;T.Ito
  2. The Theory of Splines and their Applications J.H.Ahlberg;E.N.Nilson;J.L.Walsh
  3. Computer J v.12 Cubic spline solutions to two point boundary value problems E.L.Albasiny;W.D.Hoskins
  4. Intern. J. Computer Math. v.62 Spine Solutions for system of second-order boundary-value problems E.A.Al-Said
  5. J. Nat. Geometry v.12 Quadratic spline solutions of two point boundary value problems E.A.Al-Said
  6. Smooth spline solutions for tow-point boundary value problems E.A.Al-Said
  7. Korean J. Comput. Appl. Math. v.5 Numerical solutions for system of second order boundary value problems E.A.Al-Said;M.A.Noor;A.A.Al-Shejari
  8. SIAM Numerical Solution of Boundary Value Problems for Ordinary Differential Equations U.M.Ascher;R.M.Mettheij;R.D.Russell
  9. Computer J. v.11 Piecewise cubic interpolation and two point boundary value problems W.G.Bickley
  10. The Numerical Treatment of Differential Equations L.Collatz
  11. Theory and Computer Applications, Numerical Mathematics C.Froberg
  12. Computer J. v.12 The use of cubic splines in the solution of two-point boundary value problems D.J.Fyfe
  13. Discrete Variable Methods in Ordinary Differential Equations P.Henrici
  14. IMA J. Numer. Anal v.2 Collocation with quadratic and cubic splines A.K.Khalifa;J.C.Eilbeck
  15. IMA J. Numer. Anal. v.11 Solving two-point boundary value problems with spline functions G.Mullenheim
  16. Int. J. Engng. Sci. v.25 Cubic splines collocation methods for unilateral problems M.A.Noor;A.K.Khalifa
  17. Piecewise cubic interpolation and two-point boundary value problems v.7 M.Sakai
  18. Quadratic spline and two-point boundary value problem v.19 M.Sakai;R.A.usmani
  19. J. Approx. Theory v.55 On consistency relations for cubic spline-on-spline and their asymptotic error estimates M.Sakai;R.A.Usmani
  20. Spline Functions: Basic Theory L.Schumaker
  21. J. Engrg. Math. v.9 Bounds for the solution of a second-order differential equation with mixed boundary conditions R.A.Usmani
  22. Intern. J. Computer Math. v.26 A connection between quartic spline solution and Noumerov solution of a boundary value problem R.A.Usmani;M.Sakai
  23. J. Computer and Math. with Applic. v.6 quintic spline solution of boundary value problems R.A.Usmani;S.A.Warsi