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)
Differential transform method for solving Volterra integral equation with separable kernels. (English) Zbl 1187.45003
Summary: Volterra integral equations with separable kerenels are solved using the differential transform method. The approximate solution of this equation is calculated in the form of a series with easily computable terms. Exact solutions of linear and nonlinear integral equations have been investigated and the results illustrate the reliability and the performance of the differential transform method.

45D05Volterra integral equations
Full Text: DOI
[1] Zhou, J. K.: Differential transformation and its applications for electrical circuits, (1986)
[2] Ayaz, Fatma: Solutions of the system of differential equations by differential transform method, Appl. math. Comput. 147, 547-567 (2004) · Zbl 1032.35011 · doi:10.1016/S0096-3003(02)00794-4
[3] Ayaz, Fatma: Application of differential transform method to differential-algebraic equations, Appl. math. Comput. 152, 649-657 (2004) · Zbl 1077.65088 · doi:10.1016/S0096-3003(03)00581-2
[4] Arikoglu, A.; Ozkol, I.: Solution of boundary value problems for integro-differential equations by using differential transform method, Appl. math. Comput. 168, 1145-1158 (2005) · Zbl 1090.65145 · doi:10.1016/j.amc.2004.10.009
[5] Bildik, N.; Konuralp, A.; Bek, F.; Kucukarslan, S.: Solution of different type of the partial differential equation by differential transform method and Adomian’s decomposition method, Appl. math. Comput. 127, 551-567 (2006) · Zbl 1088.65085 · doi:10.1016/j.amc.2005.02.037
[6] Arikoglu, A.; Ozkol, I.: Solution of difference equations by using differential transform method, Appl. math. Comput. 173, No. 1, 126-136 (2006) · Zbl 1148.65310
[7] Arikoglu, A.; Ozkol, I.: Solution of differential--difference equations by using differential transform method, Appl. math. Comput. 181, No. 1, 153-162 (2006) · Zbl 1148.65310 · doi:10.1016/j.amc.2006.01.022
[8] Hassan, I. H.: Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems, Chaos solitons fractals 36, No. 1, 53-65 (2008) · Zbl 1152.65474 · doi:10.1016/j.chaos.2006.06.040
[9] Liu, H.; Song, Y.: Differential transform method applied to high index differential-algebraic equations, Appl. math. Comput. 184, No. 2, 748-753 (2007) · Zbl 1115.65089 · doi:10.1016/j.amc.2006.05.173