hp -version collocation method for a class of nonlinear Volterra\n integral equations of the first kind

2018/10/01 by Khadijeh Nedaiasl, Nedaiasl, Khadijeh, Raziyeh Dehbozorgi +3
Mathematics · #45D05 #47H30 #65L60 #65L70 #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1810.00730

openalex publication_date 2018/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we present a collocation method for nonlinear Volterra\nintegral equation of the first kind. This method benefits from the idea of\nhp-version projection methods. We provide an approximation based on the\nLegendre polynomial interpolation. The convergence of the proposed method is\ncompletely studied and an error estimate under the L²-norm is provided.\nFinally, several numerical experiments are presented in order to verify the\nobtained theoretical results.\n

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