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Lukonde, Alpha Peter, Emadifar, Homan. (1405). Optimal Solution of Volterra-Fredholm Integral Equations Based on the Clique and Pell-Lucas Series Collocation Method. فصلنامه علمی زیست فناوری گیاهان زراعی, (), -. doi: 10.30473/coam.2026.76783.1375
Alpha Peter Lukonde; Homan Emadifar. "Optimal Solution of Volterra-Fredholm Integral Equations Based on the Clique and Pell-Lucas Series Collocation Method". فصلنامه علمی زیست فناوری گیاهان زراعی, , , 1405, -. doi: 10.30473/coam.2026.76783.1375
Lukonde, Alpha Peter, Emadifar, Homan. (1405). 'Optimal Solution of Volterra-Fredholm Integral Equations Based on the Clique and Pell-Lucas Series Collocation Method', فصلنامه علمی زیست فناوری گیاهان زراعی, (), pp. -. doi: 10.30473/coam.2026.76783.1375
Lukonde, Alpha Peter, Emadifar, Homan. Optimal Solution of Volterra-Fredholm Integral Equations Based on the Clique and Pell-Lucas Series Collocation Method. فصلنامه علمی زیست فناوری گیاهان زراعی, 1405; (): -. doi: 10.30473/coam.2026.76783.1375

Optimal Solution of Volterra-Fredholm Integral Equations Based on the Clique and Pell-Lucas Series Collocation Method

Control and Optimization in Applied Mathematics
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 26 خرداد 1405    اصل مقاله (2.02 M)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.30473/coam.2026.76783.1375
نویسندگان
Alpha Peter Lukonde1؛ Homan Emadifar* 2، 3
1Department of Mathematics, Faculty of Science, Karadeniz Technical University, Trabzon, Turkiye
2Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai-602 105, Tamil Nadu, India
3Department of Basic Sciences, Technical and Vocational University (TVU), Tehran, Iran
چکیده
This study presents a numerical technique for solving Volterra--Fredholm integral equations of the second kind. The solution is approximated via two independent polynomial bases, namely the Pell--Lucas polynomials and the Clique polynomials, each paired with a collocation discretisation. Both approaches are evaluated under two distinct sets of collocation points: standard equally spaced points and Chebyshev--Gauss--Lobatto points, the latter included for comparative purposes. Solution accuracy is assessed through the L2 and L∞ norms, the absolute error, and the root mean squared error (RMSE), while an upper bound error analysis is provided to establish convergence. Numerical experiments confirm that both methods achieve progressively higher accuracy as the degree N of the approximating polynomial series increases. Where applicable, the results are benchmarked against those reported in the existing literature. All numerical findings are presented in tabular and graphical form.

تازه های تحقیق
  • A unified polynomial collocation framework is developed for Volterra-Fredholm integral equations.
  • The Pell-Lucas and Clique polynomial bases are compared under standard and Chebyshev-Gauss-Lobatto nodes.
  • An upper bound error estimate is derived and validated without requiring the exact solution.
  • Both methods achieve exponential decreases in error as the polynomial degree N increases.
  • The proposed approach outperforms several existing collocation methods reported in the literature.
کلیدواژه‌ها
Volterra--Fredholm integral equations؛ Collocation points؛ Optimization؛ Pell--Lucas polynomials؛ Clique polynomials
مراجع

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