23
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

The numerical solution of differential equations with retarded argument by means of natural spline functions of even degree

, &
Pages 245-262 | Received 12 Jul 1995, Published online: 19 Mar 2007

References

  • Ahlberg , J. H. , Nilson , E. N. and Walsh , J. L. 1967 . The theory of splines and their applications , New York : Academic Press .
  • Blaga , P. and Micula , G. 1993 . Polynomial natural spline functions of even degree . Mathematica , XXXVIII ( 2 ) : 31 – 40 . Studia Univ. “Babeş,-Bolyai”
  • Blaga , P. , Micula , G. and Akça , H. On the use of spline functions of even degree for the numerical solution of the delay differential equations , to appear
  • Bleyer , A. 1978 . On global methods to solve difference-differential equation with retarded arguments . Elec. Eng. , 22 : 2 – 3 . Periodica Polytechnica, Techn. Univ. of Budapest
  • El-Safty , A. and Abo-Hasha , S. M. 1900 . On the application of spline functions to initial value problems with retarded argument . Inter. J. Computer Math. , 32 : 173 – 179 .
  • El Tarazi , M. N. and Karaballi , A. A. 1990 . On even-degree splines with applications to quadratures . J. Approx. Theory , 60 : 157 – 167 .
  • Feldstein , A. and Goodman , R. 1973 . Numerical solution of ordinary differential and retarded differential equation with discontinuous derivatives . Number. Math. , 21 : 1 – 13 .
  • Henry , M. S. and Wiggins , K. 1978 . Applications of approximation theory to differential equations with deviating arguments . Pacific J. Math. , 76 : 431 – 441 .
  • Henry , M. S. and Wiggins , K. 1981 . Approximation theory methods for linear and nonlinear differential equations with deviating arguments . SIAM J. Math. Anal. , 12 : 342 – 354 .
  • Karlin , S. , Micchelli , C. A. , Pinkus , A. and Schoenberg , I. J. 1976 . Studies in spline functions and approximation theory , New York : Academic Press .
  • Kobza , J. 1992 . Quadratic splines smoothing the first derivatives . Applications of Mathematics , 37 ( 2 ) : 149 – 156 .
  • Micula G. Funcţii spline şi aplicaţii Editura tehnică Bucureşti 1978
  • Micula , G. and Akça , H. 1988 . Numerical solution of differential equations with deviating argument using spline functions . Mathematica , XXXIII : 45 – 57 . Studia Univ. “Babeş-Bolyai”
  • Micula , G. and Akça , H. 1988 . Mathematica-Revue d′Analyse Numérique et de Théorie de 1′Approximation . Approximate solution of the second order differential equations with deviating argument by spline functions , 53 ( 1 ) : 37 – 46 . Tome 30
  • Micula G. Gorenflo R. Theory and applications of spline functions Part 1 and Part II, Mathematik, Serie A Preprint Nr. A-91-33 Freie Universitat Berlin Fachbereich Mathematik, Berlin 1991
  • Nürnberger , G. 1989 . Approximation by spline functions , Berlin-Heidelberg-New York-London-Paris-Tokyo-Hong Kong : Springer-Verlag .
  • Schmidt , K. 1972 . Delay and functional differential equations and their applications , New York : Academic Press .
  • Schultz , M. H. and Varga , R. S. 1967 . L-splines, Numer. Math. , 10 : 345 – 369 .
  • Schumaker , L. 1981 . “ Basic theory ” . In Spline functions , New York-Chichester-Brisbane-Toronto : Wiley .
  • Stečkin S. B. Subotin Ju. N. Splines in mathematics of computation Nauka, Moscow Russian 1976
  • Zavjalov S. Ju. Kvasov V. J. Miroşnicenko V. L. Methods of the spline functions Nauka, Moscow Russian 1980

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.