zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Numerical solution of nonlinear Volterra-Fredholm integro-differential equations via direct method using triangular functions. (English) Zbl 1189.65306
Summary: An effective direct method to determine the numerical solution of the specific nonlinear Volterra-Fredholm integro-differential equations is proposed. The method is based on new vector forms for representation of triangular functions and its operational matrix. This approach needs no integration, so all calculations can be easily implemented. Some numerical examples are provided to illustrate the accuracy and computational efficiency of the method.
MSC:
65R20Integral equations (numerical methods)
45J05Integro-ordinary differential equations
34K28Numerical approximation of solutions of functional-differential equations
45B05Fredholm integral equations
45D05Volterra integral equations
65L05Initial value problems for ODE (numerical methods)
References:
[1]Maleknejad, K.; Hadizadeh, M.: The numerical analysis of Adomian’s decomposition method for nonlinear Volterra integral and integro-differential equations, International journal of engineering science, iran university of science technology 8, No. 2a, 33-48 (1997)
[2]Wazwaz, A. M.: A first course in integral equations, (1997) · Zbl 0924.45001
[3]Brunner, H.: Collocation method for Volterra integral and relation functional equations, (2004)
[4]Çerdik-Yaslan, H.; Akyüz-Daşcioğlu, A.: Chebyshev polynomial solution of nonlinear Fredholm-Volterra integro-differential equations, Journal of arts and sciences, cankaya university 5, 89-101 (2006)
[5]Delves, L. M.; Mohamed, J. L.: Computational methods for integral equations, (1985)
[6]Maleknejad, K.; Mahmoudi, Y.: Taylor polynomial solution of high-order nonlinear Volterra–Fredholm integro-differential equations, Applied mathematics and computation 145, 641-653 (2003) · Zbl 1032.65144 · doi:10.1016/S0096-3003(03)00152-8
[7]Babolian, E.; Masouri, Z.; Hatamzadeh-Varmazyar, S.: New direct method to solve nonlinear Volterra–Fredholm integral and integro differential equation using operational matrix with block-pulse functions, Progress in electromagnetics research B 8, 59-76 (2008)
[8]Sepehrian, B.; Razzaghi, M.: Single-term Walsh series method for the Volterra integro-differential equations, Engineering analysis with boundary elements 28, 1315-1319 (2004) · Zbl 1081.65551 · doi:10.1016/j.enganabound.2004.05.001
[9]Deb, A.; Dasgupta, A.; Sarkar, G.: A new set of orthogonal functions and its application to the analysis of dynamic systems, Journal of the franklin institute 343, 1-26 (2006) · Zbl 1173.33306 · doi:10.1016/j.jfranklin.2005.06.005
[10]Babolian, E.; Mokhtari, R.; Salmani, M.: Using direct method for solving variational problems via triangular orthogonal functions, Applied mathematics and computation 191, 206-217 (2007) · Zbl 1193.65196 · doi:10.1016/j.amc.2007.02.080