# 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 linear Volterra integral equations system of the second kind. (English) Zbl 1148.65101
Summary: There are several numerical approaches for solving systems of linear Volterra integral equations of the second kind. We present a method for numerical solution of a system of linear Volterra integral equations based on the power series method, the major advantage of which is being derivative-free. Also, this method reproduces the analytical solution when the exact solution is a polynomial. The numerical results prove that the presented method is very effective and simple. The software used for the numerical calculations in this study was MATLAB$^{\circledR}7.4$.

##### MSC:
 65R20 Integral equations (numerical methods) 45F05 Systems of nonsingular linear integral equations
Matlab
Full Text:
##### References:
 [1] Burton, T. A.: Volterra integral and differential equations. (2005) · Zbl 1075.45001 [2] Maleknejad, K.; Aghazadeh, N.: Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method. Appl. math. Comput. 161, 915-922 (2005) · Zbl 1061.65145 [3] Yalsinbas, S.: Taylor polynomial solutions of nonlinear Volterra -- Fredholm integral equations. Appl. math. Comput. 127, 195-206 (2002) · Zbl 1025.45003 [4] Delves, L. M.; Mohamed, J. L.: Computational methods for integral equations. (1985) · Zbl 0592.65093 [5] Maleknejad, K.; Kajani, M. T.; Mahmoudi, Y.: Numerical solution of Fredholm and Volterra integral equation of the second kind by using Legendre wavelets. Kybernetes 32, No. 9 -- 10, 1530-1539 (2003) · Zbl 1059.65127 [6] Sezer, M.: Taylor polynomial solution of Volterra integral equations. Int. J. Math. edu. Sci. technol. 25, No. 5, 625 (1994) · Zbl 0823.45005 [7] Brunner, H.: Collocation method for Volterra integral and related functional equations. (2004) · Zbl 1059.65122 [8] Maleknejad, K.; Sohrabi, S.; Rostami, Y.: Numerical solution of nonlinear Volterra integral equations of the second kind by using Chebyshev polynomials. Appl. math. Comput. 188, 123-128 (2007) · Zbl 1114.65370 [9] Ghasemi, M.; Kajani, M. Tavassoli; Bobolian, E.: Numerical solutions of the nonlinear Volterra -- Fredholm integral equations by using homotopy perturbation method. Appl. math. Comput. 188, 446-449 (2007) · Zbl 1114.65367 [10] Rabbani, M.; Maleknejad, K.; Aghazadeh, N.: Numerical computational solution of the Volterra integral equations system of the second kind by using an expansion method. Appl. math. Comput. 187, 1143-1146 (2007) · Zbl 1114.65371