Hybrid collocation method for some classes of second-kind nonlinear weakly singular integral equations

Mahmoodi Darani, Narges

doi:10.22034/cmde.2022.47657.1992

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	Hybrid collocation method for some classes of second-kind nonlinear weakly singular integral equations
Computational Methods for Differential Equations
مقاله 14، دوره 11، شماره 1، فروردین 2023، صفحه 183-196 اصل مقاله (417.81 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.47657.1992
نویسنده
Narges Mahmoodi Darani
Department of mathematics‎, ‎Hashtgerd branch‎, ‎Islamic Azad University‎, ‎Hashtgerd‎, ‎Iran.
چکیده
In the current study, a fast, accurate, and reliable numerical scheme for approximating second-kind nonlinear Fredholm, Volterra, and Fredholm-Volterra integral equations with a weakly singular kernel and invertible nonlinearity is presented. The computational approach is based upon function, especially the hybrid one. Hybrid functions give us the opportunity to achieve an appropriate solution by adjusting a suitable order for polynomials’ degrees and block-pulse functions. The basic idea of this method is based on using the invertibility of the nonlinear function as a benefit to reduce the total error and simplify the procedure. The scheme reduces these types of equations to nonlinear systems of algebraic equations. Convergence analysis of the method under the infinity norm is wellstudied. Numerical results indicate the superiority of the present method compared with another existing method in the literature
کلیدواژه‌ها
Hybrid functions؛ Collocation scheme؛ Weakly singular kernel؛ Nonlinear Fredholm-Volterra integral equation؛ Convergence analysis

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Hybrid collocation method for some classes of second-kind nonlinear weakly singular integral equations