Abstract
In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.
Highlights
In many problems, the Volterra integral equations (VIEs) arise from the real life, such as population dynamics, feedback control theory, and fluid dynamics etc. [1]
Many applications of engineering or physics can often lead to Volterra integral equations
Applied the standard spectral Galerkin polynomial method and a variant to solve a weakly singular for the (VIEs). [10] extended the single-step pseudospectral method for the (VIEs-2k) to the multistep pseudo-spectral method. [11] used the Galerkin weight residual numerical method with Chebyshev polynomials and Touchard polynomials as a trial function to obtain a numerical solution for the (IEs)
Summary
The Volterra integral equations (VIEs) arise from the real life, such as population dynamics, feedback control theory, and fluid dynamics etc. [1]. Applied the standard spectral Galerkin polynomial method and a variant to solve a weakly singular for the (VIEs). Touchard polynomials method is used to solve (LVIEs) numerically. After computing the integrations (integration methods have been mentioned in the given examples) of the Eq [12] the unknown coefficients of the (TPs) are found by selecting ζ λ By applying an algorithm of the presented method which is described in the above section for this example in case n= 2, have:. Solve these equations by using Gauss elimination, and the coefficients are: θ0 = 0.51318, −0.48950.
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