TY - JOUR
ID - 15640
TI - An efficient numerical approach for solving nonlinear Volterra integral equations
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Salehi, Behnam
AU - Nouri, Kazem
AU - Torkzadeh, Leila
AD - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P.O.Box 35195-363, Semnan, Iran.
Y1 - 2023
PY - 2023
VL - 11
IS - 3
SP - 615
EP - 629
KW - Chebyshev cardinal wavelets
KW - Operational matrix
KW - Integral equation
DO - 10.22034/cmde.2022.52804.2226
N2 - This study deals with a numerical solution of a nonlinear Volterra integral equation of the first kind. The method of this research is based on a new kind of orthogonal wavelets, called the Chebyshev cardinal wavelets. These wavelets known as new basis functions contain numerous beneficial features like orthogonality, spectral accuracy, and cardinality. In addition, we assume an expansion of the terms of Chebyshev cardinal wavelets within unknown coefficients as a substitute for an unknown solution. Relatively, considering the mentioned expansion and the cardinality feature within the generated operational matrix of the introduced wavelets, a system of nonlinear algebraic equations is extracted for the stated problem. Finally, by solving the yielded system, the estimated solution results.
UR - https://cmde.tabrizu.ac.ir/article_15640.html
L1 - https://cmde.tabrizu.ac.ir/article_15640_de8869ed6543e8755d94b9de2e56e4d1.pdf
ER -