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Salehi, Behnam, Nouri, Kazem, Torkzadeh, Leila. (1402). An efficient numerical approach for solving nonlinear Volterra integral equations. سامانه مدیریت نشریات علمی, 11(3), 615-629. doi: 10.22034/cmde.2022.52804.2226
Behnam Salehi; Kazem Nouri; Leila Torkzadeh. "An efficient numerical approach for solving nonlinear Volterra integral equations". سامانه مدیریت نشریات علمی, 11, 3, 1402, 615-629. doi: 10.22034/cmde.2022.52804.2226
Salehi, Behnam, Nouri, Kazem, Torkzadeh, Leila. (1402). 'An efficient numerical approach for solving nonlinear Volterra integral equations', سامانه مدیریت نشریات علمی, 11(3), pp. 615-629. doi: 10.22034/cmde.2022.52804.2226
Salehi, Behnam, Nouri, Kazem, Torkzadeh, Leila. An efficient numerical approach for solving nonlinear Volterra integral equations. سامانه مدیریت نشریات علمی, 1402; 11(3): 615-629. doi: 10.22034/cmde.2022.52804.2226

An efficient numerical approach for solving nonlinear Volterra integral equations

Computational Methods for Differential Equations
مقاله 13، دوره 11، شماره 3، شهریور 2023، صفحه 615-629    اصل مقاله (1.59 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.52804.2226
نویسندگان
Behnam Salehi؛ Kazem Nouri* ؛ Leila Torkzadeh
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P.O.Box 35195-363, Semnan, Iran.
چکیده
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.
کلیدواژه‌ها
Chebyshev cardinal wavelets؛ Operational matrix؛ Integral equation
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