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Numerical solution of a class of third-kind Volterra integral equations using Jacobi wavelets
- Source :
- Repositório Científico de Acesso Aberto de Portugal, Repositório Científico de Acesso Aberto de Portugal (RCAAP), instacron:RCAAP
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- We propose a spectral collocation method, based on the generalized Jacobi wavelets along with the Gauss-Jacobi quadrature formula, for solving a class of third-kind Volterra integral equations. To do this, the interval of integration is first transformed into the interval [-1,1], by considering a suitable change of variable. Then, by introducing special Jacobi parameters, the integral part is approximated using the Gauss-Jacobi quadrature rule. An approximation of the unknown function is considered in terms of Jacobi wavelets functions with unknown coefficients, which must be determined. By substituting this approximation into the equation, and collocating the resulting equation at a set of collocation points, a system of linear algebraic equations is obtained. Then, we suggest a method to determine the number of basis functions necessary to attain a certain precision. Finally, some examples are included to illustrate the applicability, efficiency, and accuracy of the new scheme.<br />Comment: This is a preprint of a paper whose final and definite form is with 'Numer. Algorithms', Print ISSN 1017-1398, Electronic ISSN 1572-9265, available at [https://www.springer.com/journal/11075]. Submitted 12-Oct-2019; Revised 17-Dec-2019; Accepted 11-Feb-2020
- Subjects :
- Applied Mathematics
Numerical analysis
Third-kind Volterra integral equations
Jacobi wavelets
Collocation points
34D05, 45E10, 65T60
Gauss–Jacobi quadrature
Basis function
Numerical Analysis (math.NA)
Volterra integral equation
Quadrature (mathematics)
symbols.namesake
Algebraic equation
Wavelet
FOS: Mathematics
symbols
Gaussian quadrature
Applied mathematics
Mathematics - Numerical Analysis
Mathematics
Subjects
Details
- ISSN :
- 15729265 and 10171398
- Volume :
- 86
- Database :
- OpenAIRE
- Journal :
- Numerical Algorithms
- Accession number :
- edsair.doi.dedup.....c55e747b5a5dbca1c1c9dd873b3104bb