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)
Numerical solution of the nonlinear Volterra integro-differential equations by the tau method. (English) Zbl 1119.65123
Summary: We use the operational approach to the tau method for solving nonlinear Volterra integro-differential equations with analytic function coefficients with initial or boundary conditions. We do this without linearizing the nonlinear terms. We introduce an error estimation of the method. We give some examples to clarify the efficiency and high accuracy of the method.

65R20Integral equations (numerical methods)
45J05Integro-ordinary differential equations
45G10Nonsingular nonlinear integral equations
Full Text: DOI
[1] Delves, L. M.; Mohamed, J. L.: Computational methods for integral equations. (1985) · Zbl 0592.65093
[2] Ortiz, E. L.; Pun, K. S.: Numerical solution of nonlinear partial differential equations with the tau method. J. comput. Appl. math. 12, 511-516 (1985) · Zbl 0579.65124
[3] Ortiz, E. L.; Samara, L.: An operational approach to the tau method for the numerical solution of nonlinear differential equations. Computing 27, 15-25 (1981) · Zbl 0449.65053
[4] Ortiz, E. L.; Aliabadi, M. H.: Numerical treatment of moving and free boundary value problems with the tau method. Comp. math. Appl. 35, No. 8, 53-61 (1998) · Zbl 0999.65110
[5] Pour-Mahmoud, J.; Rahimi-Ardabili, M. Y.; Shahmorad, S.: Numerical solution of the system of Fredholm integro-differential equations by the tau method. Appl. math. Comput. 168, 465-478 (2005) · Zbl 1082.65600
[6] Ortiz, E. L.: On the numerical solution of nonlinear and functional differential equations with the tau method. Lecture notes in mathematics 679, 127-139 (1978)
[7] Hosseini, S. M.; Shahmorad, S.: A matrix formulation of the tau method and Volterra linear integro-differential equations. Korean J. Comput. appl. Math. 9, No. 2, 497-507 (2002) · Zbl 1005.65148
[8] Hosseini, S. M.; Shahmorad, S.: Numerical solution of a class of integro-differential equations by the tau method with an error estimation. Appl. math. Comput. 136, 559-570 (2003) · Zbl 1027.65182
[9] Razzaghi, M.; Yousefi, S.: Legendre wavelets method for the nonlinear Volterra Fredholm integral equations. Math. comput. Simul. 70, 1-8 (2005) · Zbl 1205.65342
[10] Wazwaz, A. M.: A reliable algorithm for solving boundary value problems for higher order integro-differential equations. Appl. math. Comput. 118, 327-342 (2001) · Zbl 1023.65150