Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Approximate solution of the differential equation $ y\sp{''}=f(x,\,y)$ with spline functions


Author: Gh. Micula
Journal: Math. Comp. 27 (1973), 807-816
MSC: Primary 65L05
Corrigendum: Math. Comp. 29 (1975), 673-674.
Corrigendum: Math. Comp. 29 (1975), 673-674.
MathSciNet review: 0331789
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An approximate spline is constructed for the solution of Cauchy's problem regarding a second-order differential equation. The existence, uniqueness and convergence of the approximate spline solution are investigated.


References [Enhancements On Off] (What's this?)

  • [1] H. B. Curry and I. J. Schoenberg, On Pólya frequency functions. IV. The fundamental spline functions and their limits, J. Analyse Math. 17 (1966), 71–107. MR 0218800 (36 #1884)
  • [2] Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons, Inc., New York-London, 1962. MR 0135729 (24 #B1772)
  • [3] F. R. Loscalzo, On the Use of Spline Functions for the Numerical Solution of Ordinary Differential Equations, Doctoral Thesis, University of Wisconsin, Madison, Wis., 1968.
  • [4] Frank R. Loscalzo and Thomas D. Talbot, Spline function approximations for solutions of ordinary differential equations, SIAM J. Numer. Anal. 4 (1967), 433–445. MR 0221756 (36 #4808)
  • [5] Gh. Micula, Fonctions spline d’approximation pour les solutions des systèmes d’équations différentielles, An. Şti. Univ. “Al. I. Cuza” Iaşi Secţ. I a Mat. (N.S.) 17 (1971), 139–155 (French, with Romanian summary). MR 0309315 (46 #8425)
  • [6] Manabu Sakai, Spline interpolation and two-point boundary value problems, Mem. Fac. Sci. Kyushu Univ. Ser. A 24 (1970), 17–34. MR 0273826 (42 #8702)
  • [7] E. Schechter, Error bounds in the numerical integration of differential equations., Studia Univ. Babeş-Bolyai Ser. Math.-Mech. 15 (1970), no. 1, 47–53 (English, with Romanian and Russian summaries). MR 0266437 (42 #1343)
  • [8] I. J. Schoenberg, On spline functions, Inequalities (Proc. Sympos. Wright-Patterson Air Force Base, Ohio, 1965), Academic Press, New York, 1967, pp. 255–291. MR 0223801 (36 #6848)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65L05

Retrieve articles in all journals with MSC: 65L05


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1973-0331789-X
PII: S 0025-5718(1973)0331789-X
Keywords: Differential equation, Cauchy problem, spline function, consistency relations, fixed point, discrete multistep method, stable method, convergence
Article copyright: © Copyright 1973 American Mathematical Society