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Manafian, Jalil, Bolgar, Peyman. (1405). Numerical idea to solve three-dimensional nonlinear Volterra integral equations with 3D-Legendre polynomials. سامانه مدیریت نشریات علمی, 14(1), 361-373. doi: 10.22034/cmde.2025.65630.3028
Jalil Manafian; Peyman Bolgar. "Numerical idea to solve three-dimensional nonlinear Volterra integral equations with 3D-Legendre polynomials". سامانه مدیریت نشریات علمی, 14, 1, 1405, 361-373. doi: 10.22034/cmde.2025.65630.3028
Manafian, Jalil, Bolgar, Peyman. (1405). 'Numerical idea to solve three-dimensional nonlinear Volterra integral equations with 3D-Legendre polynomials', سامانه مدیریت نشریات علمی, 14(1), pp. 361-373. doi: 10.22034/cmde.2025.65630.3028
Manafian, Jalil, Bolgar, Peyman. Numerical idea to solve three-dimensional nonlinear Volterra integral equations with 3D-Legendre polynomials. سامانه مدیریت نشریات علمی, 1405; 14(1): 361-373. doi: 10.22034/cmde.2025.65630.3028

Numerical idea to solve three-dimensional nonlinear Volterra integral equations with 3D-Legendre polynomials

Computational Methods for Differential Equations
مقاله 25، دوره 14، شماره 1، فروردین 2026، صفحه 361-373    اصل مقاله (507.71 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.65630.3028
نویسندگان
Jalil Manafian* ؛ Peyman Bolgar
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
چکیده
In this paper, a three-dimensional Legendre polynomial (3D-LPs) is used for solving the nonlinear three-dimensional Volterra integral equations (VIEs). Converting the main problem to a nonlinear algebraic system using 3D-LPs, which can be generalized to equations in higher dimensions, then the nonlinear system will be solved. Some results concerning the error analysis have been achieved. Several examples are included to demonstrate the validity and applicability of the method. Moreover, we prove a theorem and a corollary about a sufficient condition for the minimum of mean square error under the Legendre coefficients and the uniqueness of the solution of the nonlinear VIEs. In addition, illustrative examples are included to demonstrate the validity and applicability of the presented method.
کلیدواژه‌ها
Nonlinear Volterra integral equations؛ Three-dimensional Legendre polynomials؛ Nonlinear algebraic systems
مراجع
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