Exponential sum of the first kind

Numerical solution of the system of Volterra integral equations of the first kind

This paper presents a comparison between variational iteration method (VIM) and modfied variational iteration method (MVIM) for approximate solution a system of Volterra integral equation of the first kind. We convert a system of Volterra integral equations to a system of Volterra integro-di®erential equations that use VIM and MVIM to approximate solution of this system and hence obtain an appr...

Mordell’s Exponential Sum Estimate Revisited

Homotopy Perturbation Applied to System of Feredholm Integral Eqations of the First Kind

 Abstract: In this paper homotopy perturbation is applied to system of linear Fredholm integral equations of the first kind .For these systems, degenerate kernels are considered and in order to avoid successive integrations ,an easy matrix computation is derived for approximating the solution of the problem.  

ON THE EXPONENTIAL SUM WITH THE SUM OF DIGITS OF HEREDITARY BASE b NOTATION

Let b 2 be an integer and wb(n) be the sum of digits of the nonnegative integer n written in hereditary base b notation. We give optimal upper bounds for the exponential sum PN 1 n=0 exp(2⇡iwb(n)t), where t is a real number. In particular, our results imply that for each positive integer m the sequence {wb(n)}n=0 is uniformly distributed modulo m; and that for each irrational real ↵ the sequenc...

Numerical solution of two-dimensional integral equations of the first kind by multi-step methods

‎‎‎In this paper‎, ‎we develop multi-step methods to solve a class of two-dimensional nonlinear Volterra integral equations (2D-NVIEs) of the first kind‎. ‎Here‎, ‎we convert a 2D-NVIE of the first kind to a one-dimensional linear VIE of the first kind and then we solve the resulted equation numerically by multi-step methods‎. ‎We also verify convergence and error analysis of the method‎. ‎At t...