Theoretical analysis of Sinc-Nyström methods for Volterra integral equations

Theoretical analysis of Sinc-Nyström methods for Volterra integral equations

MATHEMATICAL ENGINEERING TECHNICAL REPORTS Theoretical Analysis of Sinc-Nyström Methods for Volterra Integral Equations

In this paper, three theoretical results are presented on Sinc-Nyström methods for Volterra integral equations of the first and second kind that have been proposed by Muhammad et al. On their methods, the following two points have been desired to be improved: 1) their methods include a tuning parameter hard to be found unless the solution is given, and 2) convergence has not been proved in a pr...

Theoretical analysis of a Sinc-Nyström method for Volterra integro-differential equations and its improvement

s of MMA2013 & AMOE2013, May 27–30, 2013, Tartu, Estonia c ⃝ 2013 University of Tartu THEORETICAL ANALYSIS OF A SINC-NYSTRÖM METHOD FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS AND ITS IMPROVEMENT

Theoretical analysis of Sinc-collocation methods and Sinc-Nyström methods for initial value problems

A Sinc-collocation method has been proposed by Stenger, and he also gave theoretical analysis of the method in the case of a ‘scalar’ equation. This paper extends the theoretical results to the case of a ‘system’ of equations. Furthermore, this paper proposes more efficient method by replacing the variable transformation employed in Stenger’s method. The efficiency is confirmed by both of theor...

Convergence of the Sinc method applied to Volterra integral equations

A collocation procedure is developed for the linear and nonlinear Volterra integral equations, using the globally defined Sinc and auxiliary basis functions. We analytically show the exponential convergence of the Sinc collocation method for approximate solution of Volterra integral equations. Numerical examples are included to confirm applicability and justify rapid convergence of our method.