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ON Numerical Blow-Up Solutions of Semilinear Heat Equations

This paper is concerned with the numerical blow-up solutions of semi-linear heat equations, where the nonlinear terms are of power type functions, with zero Dirichlet boundary conditions. We use explicit linear and implicit Euler finite difference schemes with a special time-steps formula to compute the blow-up solutions, and to estimate the blow-up times for three numerical experiments. Moreover, we calculate the error bounds and the numerical order of convergence arise from using these methods. Finally, we carry out the numerical simulations to the discrete graphs obtained from using these methods to support the numerical results and to confirm some known blow-up properties for the studied problems.

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Publication Date
Thu Dec 01 2016
Journal Name
Journal Of Engineering
Numerical and Experimental Investigations of the Effect of PVD and Vacuum Pressure on the Degree of Saturation

    Soft clays are generally characterized by low shear strength, low permeability and high compressibility. An effective method to accelerate consolidation of such soils is to use vertical drains along with vacuum preloading to encourage radial flow of water.  In this research numerical modeling of prefabricated vertical drains with vacuum pressure was done to investigate the effect of using vertical drains together with vacuum pressure on the degree of saturation of fully and saturated-unsaturated soft soils.  Laboratory experiments were conducted by using a specially-designed large consolidometer cell where a central drain was installed and vacuum pressure was applied. All tests were conducted

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Publication Date
Sun Dec 29 2019
Journal Name
Iraqi Journal Of Science
Cubic Trigonometric Spline for Solving Nonlinear Volterra Integral Equations

In this paper, cubic trigonometric spline is used to solve nonlinear Volterra integral equations of second kind. Examples are illustrated to show the presented method’s efficiency and convenience.

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Publication Date
Fri Dec 30 2022
Journal Name
Iraqi Journal Of Science
The Operational Matrices Methods for Solving Falkner-Skan Equations

     The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which is used to solve the Falkner-Skan equation. The nonlinear differential equation converting to a system of nonlinear equations is solved using Mathematica®12, and the approximate solutions are obtained. The efficiency of these methods was studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as  increases. Moreover, the obtained approximate solutions are compared with the numerical solution obtained by the fourth-order Runge-Kutta method (RK4), which gives  a good agreement.

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Publication Date
Wed Jul 17 2019
Journal Name
Iraqi Journal Of Science
An Approximation Technique for Fractional Order Delay Differential Equations

In this research article, an Iterative Decomposition Method is applied to approximate linear and non-linear fractional delay differential equation. The method was used to express the solution of a Fractional delay differential equation in the form of a convergent series of infinite terms which can be effortlessly computable.
The method requires neither discretization nor linearization. Solutions obtained for some test problems using the proposed method were compared with those obtained from some methods and the exact solutions. The outcomes showed the proposed approach is more efficient and correct.

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Publication Date
Wed Jun 15 2022
Journal Name
International Journal Of Agriculture Environment And Food Sciences
Functional and numerical response of Hippodamia variegata (Goeze) (Coleoptera: Coccinellidae) on Macrosiphum rosae (L.) (Hemiptera: Aphididae)

In this study, functional and numerical response tests, which are important components in the selection of biological control agent, were carried out. In functional response trials, the amount of food consumed, attack rate (a) and handling time (Th) were calculated for each developmental period, depending on the number of preys given after 24 hours. The obtained results were evaluated with the Holling. In numerical response experiments, the development of the predator insect was examined depending on the number of preys given in certain numbers (5, 10, 20, 40 and 80) and the data were recorded. This phase of the trials continued until the individuals died. At this stage of the trials, the reproductive response of the p

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Publication Date
Tue Mar 30 2021
Journal Name
Iraqi Journal Of Science
Numerical Simulation of Magnetohydrodynamic Influences on Casson Model for Blood Flow through an Overlapping Stenosed Artery

Magnetohydrodynamic (MHD) effects of unsteady blood flow on Casson fluid through an artery with overlapping stenosis were investigated. The nonlinear governing equations accompanied by the appropriate boundary conditions were discretized and solved based on a finite difference technique, using the pressure correction method with MAC algorithm. Moreover, blood flow characteristics, such as the velocity profile, pressure drop, wall shear stress, and patterns of streamlines, are presented graphically and inspected thoroughly for understanding the blood flow phenomena in the stenosed artery.

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Publication Date
Sun Feb 27 2022
Journal Name
Iraqi Journal Of Science
Continuous Classical Optimal Control of Triple Nonlinear Parabolic Partial Differential Equations

    This paper  concerns with the state and proof the existence and uniqueness theorem of triple state vector solution (TSVS) for the triple nonlinear parabolic partial differential equations (TNPPDEs) ,and triple state vector equations (TSVEs), under suitable assumptions. when the continuous classical triple control vector (CCTCV) is given by using the method of Galerkin (MGA). The existence theorem of a continuous classical optimal triple control vector (CCTOCV) for the continuous classical optimal control governing by the TNPPDEs under suitable conditions is proved.  

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Publication Date
Sun Jan 05 2014
Journal Name
Paripex - Indian Journal Of Research
Effect of heat treatment on the structural and optical properties of CuIn1-xGaxSe thin films

The structural, optical properties of cupper indium gallium selenite (CuIn1-xGaxSe) have been studied. CuIn1-xGaxSe thin films for x=0.6 have been prepared by thermal evaporation technique, of 2000±20 nm thickness, with rate of deposition 2±0.1 nm/sec, on glass substrate at room temperature. Heat treatment has been carried out in the range (373-773) K for 1 hour. It demonstrated from the XRD method that all the as-deposited and annealed films have polycrystalline structure of multiphase. The optical measurement of the CIGS thin films conformed that they have, direct allowed energy gap equal to 1.7 eV. The values of some important optical parameters of the studied films such as (absorption coefficient, refractive index, extinction coeffici

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Publication Date
Wed Jun 15 2022
Journal Name
Journal Of Baghdad College Of Dentistry
Effect of Optiglaze Coating on the Staphylococcus aurous and Porosity of Heat Cured Acrylic Material

Background: Polishing technique for acrylic resin material have great effect on properties of acrylic material and bacterial colonization such as staphylococcus aurous, which are responsible for many acrylic prosthetic infections such as the commonly ocular infections. Ineffective polishing technique could affect roughness and subsequently porosity of acrylic materials.So, a new effective method for polishing acrylic was used depending on the use of optiglaze coating material. So, this study aimed to evaluate the effect of optiglaze polishing on porosity of acrylic resin material and staphylococcus aurous activity in comparison to conventional polishing technique. 

Materials and methods: Specimen(n=120) were prepared :20 spe

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Publication Date
Thu Jun 01 2017
Journal Name
Iosr Journal Of Pharmacy And Biological Sciences
Effect of Nano Silicon Dioxide Addition on Some Properties of Heat Vulcanized Maxillofacial Silicone Elastomer

Abstract : Silicone elastomer is widely used as the material of choice for fabricating maxillofacial prosthesis. However, silicone properties are far from ideal; low tear strength, low tensile strength and insufficient elasticity are the most undesirable properties. The purpose of this study was to evaluate the effect of addition of nano SiO2filler on tear strength, tensile strength, elongation at break, hardness and color of Cosmesil M-511 HTV maxillofacial silicone elastomer. Nano SiO2was added to the silicone base in concentrations of 4%, 5% and 6% by weight. Silicone with 0% nano filler served as a control. Tear test was done according to ISO 34-1. Tensile and elongation test was done according to ISO 37. Shore A hardness test was done

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