zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The numerical solution of third-order boundary-value problems using quintic splines. (English) Zbl 1027.65100
Summary: We present a fourth-order method based on quintic splines for the solution of third-order linear and nonlinear boundary-value problems (BVPs) of the form $y'''=f(x,y),a\leqslant x\leqslant b$, subject to the boundary conditions $y(a)=k_1, y'(a)=k_2, y(b)=k_3$. Numerical examples are given to illustrate the method and their convergence.

65L10Boundary value problems for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
65L20Stability and convergence of numerical methods for ODE
Full Text: DOI
[1] Ahlberg, J. M.; Nilson, E. N.; Wash, J. L.: The theory of splines and their applications. (1967) · Zbl 0158.15901
[2] J. Rashidinia, Applications of splines to the numerical solution of differential equations, Ph.D. thesis, Aligarh Muslim University, Aligarh, 1994
[3] Tirmizi, S. I. A.: On numerical solution of third-order boundary-value problems. Commun. appl. Numer. math. 7, 309-313 (1991) · Zbl 0727.65069
[4] Caglar, H. N.; Caglar, S. H.; Twizell, E. H.: The numerical solution of third-order boundary-value problems with fourth-degree B-spline functions. Int. J. Comput. math. 71, 373-381 (1999) · Zbl 0929.65048
[5] Jain, M. K.: Numerical solution of differential equations. (1984) · Zbl 0536.65004