OALib Journal
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Feb 13, 2020Open    AccessArticle

Quasiquadrature Solution of the Linear Integral Equations of the Second Kind in the Class of Integrable Functions

Igor Petrovich Dobrovolsky
The analog of the quadrature solution of the equation of the second kind is considered. Fundamental difference from classical quadrature formulas is as follows. On segments of the chosen grid not values of functions, but their integral average values are used. Equations of Fredholm and Volterra are considered. The graphical representation of the solution is discussed. Computing examples show expediency of such approach in appropriate cases.


Sep 12, 2019Open    AccessArticle

Quasi-Quadrature Solution of Integral Equations Fredholm of the Second Kind in the Class of Integrable Functions

Igor Petrovich Dobrovolsky
The analog of the quadrature solution of the equation of Fredholm of the second kind is considered. Fundamental difference from classical quadrature formulas is as follows. On segments of the chosen grid not values of functions, but their integral average values are used. Computing examples show expediency of such approach in appropriate cases.


Aug 29, 2019Open    AccessArticle

The Power Integrations of Trigonometric and Hyperbolic Functions

Ahmed M. Ali, Omar M. Abd-Alkanee
For importance of the trigonometric integrals, we have in this paper finding a series of power, some of trigonometric functions that did not exist before in the first section. As shown in the Section two, where, the integration of trigono-metric function with power n has been achieved and approved, this result is considered as the first achievement. while in the third section we find integrals
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Dec 15, 2017Open    AccessArticle

Collocation Technique for Numerical Solution of Integral Equations with Certain Orthogonal Basis Function in Interval [0, 1]

O. L. Babasola, I. Irakoze
This paper is concerned with the construction of a class of polynomial orthogonal with respect to the weight function w(x)=1-x2 over the interval [0,1]. The zeros of these polynomials were employed as points of co
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Dec 22, 2014Open    AccessArticle

Forced Oscillation of Neutral Impulsive Parabolic Partial Differential Equations with Continuous Distributed Deviating Arguments

Guangjie Liu, Chengyong Wang
This paper investigated oscillatory properties of solutions for nonlinear parabolic equations with impulsive effects under two different boundary conditions. By using integral averaging method, variable substitution and functional differential inequalities, we established several sufficient conditions. At last, we provided two examples to illustrate the results.


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