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)
A new algorithm for a class of singular boundary value problems. (English) Zbl 1175.65085
Summary: We present a new algorithm to solve a class of singular boundary value problems in the reproducing kernel space $W_2^3[0,1]$. The algorithm is efficiently applied to solving some model problems with the comparison between the numerical solutions and the exact solutions. It is demonstrated by the numerical examples that this algorithm is of high precision.

65L10Boundary value problems for ODE (numerical methods)
34B16Singular nonlinear boundary value problems for ODE
46E22Hilbert spaces with reproducing kernels
Full Text: DOI
[1] Mohanty, R. K.; Jha, Navnit: A class of variable mesh spline in compression methods for singularly perturbed two point singular boundary value problems. Appl. math. Comput. 168, 704-716 (2005) · Zbl 1082.65550
[2] Mohanty, R. K.; Arora, Urvashi: A family of non-uniform mesh tension spline methods for singularly perturbed two point singular boundary value problems with significant first derivatives. Appl. math. Comput. 172, 531-544 (2006) · Zbl 1088.65071
[3] Ling, Leevan; Trummer, Manfred R.: Adaptive multiquadric collocation for boundary layer problems. J. comput. Appl. math. 188, 265-282 (2006) · Zbl 1086.65078
[4] Wang, Xiao-Yun; Jiang, Yao-Lin: A general methods for solving singular perturbed impulsive differential equations with two-poing boundary conditions. Appl. math. Comput. 171, 775-806 (2005) · Zbl 1090.65094
[5] Zhang, Xinguang; Liu, Lishan: Positive solution of superlinear semipositone singular Dirichlet boundary value problems. J. math. Anal. 316, 525-537 (2006) · Zbl 1097.34019
[6] Li, Chunli; Cui, Minggen: The exact solution for solving a class nonlinear operator equations in the reproducing kernel space. Appl. math. Comp. 143, 393-399 (2003) · Zbl 1034.47030
[7] Yang, Heping: On a singular perturbation problem with two second-order turning points. J. comput. Appl. math. 190, 287-303 (2006) · Zbl 1103.34047
[8] Wong, R.; Yang, Heping: On an internal boundary layer problem. J. comp. Math. 144, 301-323 (2002) · Zbl 1012.34049
[9] Wong, R.; Yang, Heping: On a boundary-layer problem. Stud. appl. Math. 108, 369-398 (2002) · Zbl 1152.34360
[10] Wong, R.; Yang, Heping: On the ackerberg -- o’malley resonance. Stud. appl. Math. 110 (2003) · Zbl 1141.34331
[11] Minggen, Cui; Zhongxing, Deng: Solutions to the definite solution problem of differential equations in space w2l[0,1]. Adv. math. 17, No. 3, 327-328 (1986)