Abstract
Two numerical methods are proposed to solve nonlinear Volterra integral equations of the first kind. By using variable transformations, the problem is converted into linear Volterra integral equations of the second kind. These methods are implemented by utilizing Sinc quadrature, and then the problem is reduced to linear algebraic system equations. We state error analysis for the proposed methods, which show that these methods obtain exponential convergence order. Numerical examples are presented to confirm the theoretical estimation and illustrate the effectiveness of the proposed methods.
Highlights
Volterra integral equations of the first kind arise in many fields of science and engineering, for example, in diffusion problems, fluid dynamics, heat conduction problems, nonlinear dynamic systems identification, concrete problems of mechanics, et cetera
3 Sinc Nyström method for Volterra integral equations In this part, we consider the numerical solution of Eq ( )
Tomoaki Okayama and his coauthors have given the theoretical analysis of Sinc Nyström methods for linear Volterra equation in [ ] by utilizing error estimates with explicit constants for Sinc quadrature
Summary
Volterra integral equations of the first kind arise in many fields of science and engineering, for example, in diffusion problems, fluid dynamics, heat conduction problems, nonlinear dynamic systems identification, concrete problems of mechanics, et cetera. This paper is focused on proposing two numerical methods for solving a class of nonlinear Volterra integral equations of the first kind in the form x Inderdeep and Sheo presented the Haar wavelet method for numerical solution of a class of nonlinear Volterra integral equations of the first kind in [ ]. Muhammad et al [ ] presented a technique for linear integral equations using the Sinc collocation method based on the DE transformation.
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