Urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. The main objective of this paper is to solve the Urysohn type Fredholm integral equation. To do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known Legendre polynomials instead of the known function. After discretization of the problem o...

Due to the full-wave AC–DC power conversion, second-order frequency oscillations of current and voltage are created in single-phase PV-grid-connected inverters. These propagate toward input adversely affect PV utilization ratio. Large decoupling capacitors preliminary solution for coping with ripples across PVs, they decrease lifetime overall system. This paper proposes average mode control (AC...

Introduction Intensity-Modulated Radiotherapy (IMRT) is becoming an increasingly routine treatment method. IMRT can be delivered by use of conventional Multileaf Collimators (MLCs) and/or physical compensators. One of the most important factors in selecting an appropriate IMRT technique is integral dose. Integral dose is equal to the mean energy deposited in the total irradiated volume of the p...

Well-performing control loops have an integral role in efficient and sustainable industrial production. Control performance monitoring (CPM) tools are necessary to establish further process optimization preventive maintenance. Data-driven, model-free approaches studied this research by comparing the of nine CPM methods industrially relevant simulation. The robustness some is considered with var...

Integral inequalities with maxima of the unknown function are useful in the study of control theory. Known results were given for Gronwall-Bellman type integral inequalities with the maxima in the form of linear dependence on the unknown function with a single delay term. In this paper we consider a general form of nonlinear integral inequalities with the maxima and more than one delay terms. R...

We propose a method to treat the three-gluon self-interaction vertex in the position space in D = 4− 2ǫ dimensions. As an example, we calculate a two-loop contribution to auxiliary Lcc vertex in the Landau gauge which contains the three-gluon vertex for SU(N) YangMills theory. We represent the integral expression as a sum of separate contributions so that each of the contributions is a double f...

the first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. this method can be applied to non integrable equations as well as to integrable ones. in this paper, the first integral method is used to construct exact solutions of the 2d ginzburg-landau equation.

in this work, we present a computational method for solving second kindnonlinear fredholm volterra integral equations which is based on the use ofhaar wavelets. these functions together with the collocation method are thenutilized to reduce the fredholm volterra integral equations to the solution ofalgebraic equations. finally, we also give some numerical examples that showsvalidity and applica...

in this paper, using the tools involving measures of noncompactness and darbo fixed point theorem forcondensing operator, we study the existence of solutions for a large class of generalized nonlinear quadraticfunctional integral equations. also, we show that solutions of these integral equations are locally attractive.furthermore, we present an example to show the efficiency and usefulness of ...