Polynomial spline collocation method for solving weakly regular Volterra integral equations of the first kind

2021/11/23 by A. Tynda, Tynda, A., Samad Noeiaghdam +3
Mathematics · Physics and Astronomy · #45H05 #65R20 #Dynamical Systems (math.DS) #Electromagnetic Scattering and Analysis #FOS: Computer and information sciences #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical Software (cs.MS) #Mathematical functions and polynomials #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2111.11706

openalex publication_date 2021/11/23 · openalex created_date 2022/11/02 · openalex updated_date 2026/07/28

Abstract

The polynomial spline collocation method is proposed for solution of Volterra integral equations of the first kind with special piecewise continuous kernels. The Gauss-type quadrature formula is used to approximate integrals during the discretisation of the proposed projection method. The estimate of accuracy of approximate solution is obtained. Stochastic arithmetics is also used based on the Contrôle et Estimation Stochastique des Arrondis de Calculs (CESTAC) method and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library. Applying this approach it is possible to find optimal parameters of the projective method. The numerical examples are included to illustrate the efficiency of proposed novel collocation method.

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