Integral Equation Of Second Type Research Articles

On the solution of the Volterra integral equation of second type for the error term in an asymptotic formula for arithmetical functions

In 2010, J.Kaczorowski and K.Wiertelak considered the Volterra integral equation of second type for the remainder term in the asymptotic formula for the Euler totient function. The author found that the consideration made by them holds for other remainder terms in the asymptotic formula having certain common properties. In this paper, we first consider the pair of complex-valued arithmetical functions $(a(n),b(n))$ satisfying $b(n) \hspace{-0.1cm} = \sum_{d|n} a(d)n/d$. We prove that the solution of the Volterra integral equation of second type for the error term in the asymptotic formula for $b(n)$ can be obtained when $a(n)$ satisfies some special condition.

Galerkin-Collocation Manner for The System of Nonlinear Volterra Integral Equations of The Second Type Using Exponential Function

In this research, we introduce a new scheme stem on exponential function as test function of Galerkin-Collocation manner (GCm) for disbanding system of nonlinear Volterra integral equations of second type (NLVIEK2) numerically. Our manner involves of diminution the trouble to a collection of nonlinear system of equations. Arithmetic epitome are offered for corroborate the validation of the suggested illation and arithmetic disbanding are contrast with the located manner.

Hitting Times with Respect to Time-Dependent Barriers

In this short note, we prove that the distribution function of a hitting time of a Brownian Motion with respect to a differentiable, lower threshold solves a Volterra integral equation of second type. Moreover, we give an explicit expression for the kernel of the integral equation in terms of the boundary function and demonstrate how to find a solution of that equation (i.e. the distribution function) using Banach's Fixed-Point Theorem.As a second step, based on the first result, we find an integral representation of the terminal wealth distribution attached to the following, self-financing strategy: Let S_t be standard Geometric Brownian Motion stopped as soon as S_t hits a lower, time-dependent threshold. Then invest all of S_t in the money market account.

Fredholm partial integral equations of second type with degenerate kernel

In this paper we study the solvability of the Fredholm partial integral equations of second type with degenerate kernels.

Bounds for solutions of integral equations of second type

Bounds for solutions of integral equations of second type

On the probability model for solving some integral equations of second type

On the probability model for solving some integral equations of second type

On the solution of an integral equation of second type by the Monte-Carlo method

On the solution of an integral equation of second type by the Monte-Carlo method