Numerical approach based on Bernstein polynomials for solving mixed Volterra-Fredholm integral equations
Source abstract
Abstract
This paper provides an effective numerical technique for obtaining the approximate solution of mixed Volterra-Fredholm Integral Equations (VFIEs) of second kind. The VFIEs arise from parabolic boundary value problems, mathematical modelling of the spatio-temporal development of an epidemic, and from various physical and Engineering models. The proposed method is based on the discretization of VFIEs by Bernstein’s approximation. Some results on convergence are also established which suggests that the technique converges to a smooth approximate solution. Its remarkable accuracy properties are finally demonstrated by several examples with graphical representation.
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Research context
OpenAlex topics: Fractional Differential Equations Solutions · Iterative Methods for Nonlinear Equations · Nonlinear Differential Equations Analysis
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Mathematics, University of Sargodha 1 , Sargodha 40100, Pakistan
Department of Mathematics, The Islamia University of Bahawalpur 2 , 63100, Pakistan
Department of Mathematics, COMSATS Institute of Information Technology 3 , 57000, Pakistan
Funding
National Research Program for Universities, NRPU
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