In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.

A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

The aim of this paper is to present the numerical method for solving linear system of Fredholm integral equations, based on the Haar wavelet approach. Many test problems, for which the exact solution is known, are considered. Compare the results of suggested method with the results of another method (Trapezoidal method). Algorithm and program is written by Matlab vergion 7.

The research work covers a study of the possibility of producing porous ceramic bodies
as a thermal insulators by adding fired Dechla kaolinite (grog)to the same non burned
kaolinite.
Different weight percentage ranged between (0,15,25,35and40)from grog and sawdust
passed through mesh 50 to Deuchla-clay kaolinit.Cylindrical shape samples (30mm diameter
and 30mm height) were prepared by the semi-dry methed,moulding pressure was 50 N/mm
2
.
After drying at 110
o
c,the samples were burnet in the furnace at temperatures
900,950,1000,1050,and 1100
o
c. The sawdust burnt out and leaves air spaces which contribute
to the high thermal insulation value.
The fired samples were investigated to de

 Abstract 

The vegetative filter strips (VFS) are a useful tool used for reducing the movement of sediment and pesticide in therivers. The filter strip’s soil can help in reducing the runoff volume by infiltration. However, the characteristics of VFS (i.e., length) are not recently identified depending on the estimation of VFS modeling performance. The aim of this research is to study these characteristics and determine acorrelation between filter strip length and percent reduction (trapping efficiency) for sediment, water, and pesticide. Two proposed pesticides(one has organic carbon sorption coefficient, K_oc, of 147 L/kg which is more moveable than XXXX, and another one

With the shift of narration and the revolution against the traditional methods which were dominated by the authorial intrusion and the single narrative voice, there appeared new forms that go along with the change in methods of narration. Form becomes the representation which equips us to understand more fully aspects of existence outside of art. Form is the objectifying of idea, and its excellence depends upon its appropriateness to the idea.¹ One of the most important approaches to writing fiction is the power of point of view.

In the strategy of 'point of view' lies the secret of art and, as Norman Friedman indicates, it provides a method for distinguishing the possible degrees of authorial extinction in the narrati

Transportation Sector classified as one of the services sectors which is without the production activities cannot be complete its rule. Is act asmoving actions which operate at production and non production goals for the organization and individuals insides the country and with others, that is why this sector act as one of the main which is occupied an important status on the way the economic activities and on the level of the economic institutions the transportation work on transforming all the commodities and products from productions locations to consumption location then its effect the productivity process and create the location utility and on the level of economic it considered as one of the economic supportive structure an