In this paper we use non-polynomial spline functions to develop numerical methods to approximate the solution of 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of these method, and to compare the computed results with other known methods.

Soil is the cardinal resource for agricultural crops. Healthy soil will produce healthy plants. Since healthy soil is the important goal for the farmers, they need to select the best tillage system to achieve that goal. There are two main types of tillage systems. Conservation tillage (no-tillage farming) uses agricultural machinery that performs a double function; tillage and seed farming simultaneously. In contrast, conventional tillage farming uses multiple agricultural machines to till and seed the soil. The farmers in the northern governorates of Iraq have used the conservation farming system for a long time. However, the farmers who live in the middle and southern governorates in Iraq use conventional tillage farming. Because most of

Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained

Cooling towers is one of the most important unit in industry, they are used to dispose heat from cooling media used in the integrated units. The choice of the cooling media plays recently an important rule due to fresh-water scarcity. The use of saline as a cooling media become of growing interest, but the corrosion problem has to be taken in consideration. In this study the simultaneous effect of cooling tower operation parameters on the corrosion rate of mild-steel is considered. The role of NaCl content is found to be pronounced more than the working solution temperature and flowrate. The corrosion of mild-steel in these studied factors had shown an interesting result especially with the NaCl% content. Firstly, there was an increase in t

  The aim of this paper is to present a method for solving high order ordinary differential equations with two point's boundary condition, we propose semi-analytic technique using two-point oscillatory interpolation to construct polynomial solution. The original problem is concerned using two-point oscillatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] .  Also, many examples are presented to demonstrate the applicability, accuracy and efficiency of the method by comparing with conventional methods.

This paper is attempt to study the nonlinear second order delay multi-value problems. We want to say that the properties of such kind of problems are the same as the properties of those with out delay just more technically involved. Our results discuss several known properties, introduce some notations and definitions. We also give an approximate solution to the coined problems using the Galerkin's method.

In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth

Medicinal plants are used to treat various diseases although little is known about their toxicity. Coriandrum sativum is one of the most commonly plants that is used to treat several physiological disorders. Thus, this study was conducted to evaluate the effect of aqueous extract of C. sativum on the structure and function of liver in male albino mice. Thirty male mice were randomly divided into three groups: Group 1 untreated (control), Group 2 and 3 were administrated orally with the aqueous extract of the plant at dose 125 and 250 mg/kg. b. w. For 30 days. The effect of the extract on liver weights, biochemical parameters as well as histological study were assessed. There were no significant difference (P>0.05) observed in relative

The aqueous extract of banana fruits peal was tested for its effect on mitosis . The root tips of Allium cepa were used as plant test system and the bone marrow cells of the albino mice Mus musculus were used as mammalians test system in vivo .Root tips of Allium cepa were treated for four hours with five concentrations of the extract (5 , 10 , 20 , 40 ,60 mg / ml.).The Metaphase was arrested in all the treatments , the highest percentage ( 100 % ) was recorded in the first concentration , the last concentration caused stickiness and clumping of the chromosomes. The treatments did not cause significant difference in the mitotic index. The peals extract (5 mg /ml) was compared with the extracts of fruits bulb, leaves and r

The aqueous extract of banana fruits peal was tested for its effect on mitosis . The root tips of Allium cepa were used as plant test system and the bone marrow cells of the albino mice Mus musculus were used as mammalians test system in vivo .Root tips of Allium cepa were treated for four hours with five concentrations of the extract (5 , 10 , 20 , 40 ,60 mg / ml.).The Metaphase was arrested in all the treatments , the highest percentage ( 100 % ) was recorded in the first concentration , the last concentration caused stickiness and clumping of the chromosomes. The treatments did not cause significant difference in the mitotic index. The peals extract (5 mg /ml) was compared with the extracts of fruits bulb, leaves and roots of