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فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

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Hajimohammadi, Zeinab, Parand, Kourosh. (1405). An Efficient Computational Scheme Combining Legendre Polynomials and Deep Neural Networks for Nonlinear Integral Equations. سامانه مدیریت نشریات علمی, (), -. doi: 10.22034/cmde.2026.70547.3514
Zeinab Hajimohammadi; Kourosh Parand. "An Efficient Computational Scheme Combining Legendre Polynomials and Deep Neural Networks for Nonlinear Integral Equations". سامانه مدیریت نشریات علمی, , , 1405, -. doi: 10.22034/cmde.2026.70547.3514
Hajimohammadi, Zeinab, Parand, Kourosh. (1405). 'An Efficient Computational Scheme Combining Legendre Polynomials and Deep Neural Networks for Nonlinear Integral Equations', سامانه مدیریت نشریات علمی, (), pp. -. doi: 10.22034/cmde.2026.70547.3514
Hajimohammadi, Zeinab, Parand, Kourosh. An Efficient Computational Scheme Combining Legendre Polynomials and Deep Neural Networks for Nonlinear Integral Equations. سامانه مدیریت نشریات علمی, 1405; (): -. doi: 10.22034/cmde.2026.70547.3514

An Efficient Computational Scheme Combining Legendre Polynomials and Deep Neural Networks for Nonlinear Integral Equations

Computational Methods for Differential Equations
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 12 آبان 1405    اصل مقاله (1.48 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2026.70547.3514
نویسندگان
Zeinab Hajimohammadi* 1؛ Kourosh Parand2
1Interdisciplinary Quranic Studies Research Institute, Shahid Beheshti University, Tehran, Iran.
21. Department of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran. 2. Institute for Cognitive and Brain Sciences, Shahid Beheshti University, Tehran, Iran.
چکیده
Various phenomena in biology, physics, and engineering are modeled by differential equations. These differential equations, including partial differential equations and ordinary differential equations, can be converted and represented as integral equations. In particular, Volterra--Fredholm--Hammerstein integral equations are a main class of such integral equations, and researchers are interested in investigating and solving these equations. In this paper, we propose Legendre Deep Neural Network (LDNN) for solving nonlinear Volterra--Fredholm--Hammerstein integral equations~(V-F-H-IEs). LDNN utilizes Legendre orthogonal polynomials as activation functions in the deep structure. We present how LDNN can be used to solve nonlinear V-F-H-IEs. We show that using the Gaussian quadrature collocation method in combination with LDNN results in a novel numerical solution for nonlinear V-F-H-IEs. Several examples are given to verify the performance and accuracy of LDNN.
کلیدواژه‌ها
Deep Neural Network؛ Legendre Polynomials؛ Collocation Method؛ Volterra–Fredholm–Hammerstein integral equations (V-F-H-IEs)
آمار
تعداد مشاهده مقاله: 1


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