Abstract
In this chapter, Bernstein polynomial approximation is applied for the approximate solution of the system of Volterra-Fredholm integral equations (VFIEs) on arbitrary interval [r, s]. The proposed numerical technique reduces the given system to an algebraic linear system and can be solved using any usual numerical technique. Moreover, the stability and convergence of the proposed method is given by providing some theorems. Numerical examples are provided to illustrate the approximation and accuracy of the given technique. The comparison of approximate and exact solutions for the distinct values of the degree n is given to check the convergence rate of the proposed technique.
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The author Muhammad Basit thanks to Department of Mathematics, University of Sargodha, Pakistan for providing fruitful research environment and support.
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Khan, F., Basit, M. (2022). Numerical Method for the System of Volterra-Fredholm Integral Equations and Its Convergence Analysis. In: Abdul Karim, S.A. (eds) Intelligent Systems Modeling and Simulation II. Studies in Systems, Decision and Control, vol 444. Springer, Cham. https://doi.org/10.1007/978-3-031-04028-3_24
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DOI: https://doi.org/10.1007/978-3-031-04028-3_24
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