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Efficient computational methods for solving the nonlinear initial and boundary value problems

In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasing degree of polynomial solutions (n). In addition, the convergence of the proposed approximate methods is given based on the Banach fixed point theorem.

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Publication Date
Sun Apr 01 2018
Journal Name
Journal Of Educational And Psychological Researches
Discipline in the classroom (problems and solutions)

Research Summary

First: the problem of research and its importance

      The teacher's success in facilitating the students' learning and growth according to the educational and educational goals set out, he must identify the problems of discipline of students in the classroom in terms of sources and reasons and types and methods of prevention and treatment and the teacher to remember that success in his teaching and instruction is not completed more fully once he has the information And knowledge of the subject of the lesson, but must understand the dynamics of the group (class group) and master the skills of classroom management, su

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Publication Date
Thu Apr 27 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Numerical Solutions Of The Nonlocal Problems For The Diffusion Partial Differential Equations

    In this work, we use the explicit and the implicit finite-difference methods to solve the nonlocal problem that consists of the diffusion equations together with nonlocal conditions. The nonlocal conditions for these partial differential equations are approximated by using the composite trapezoidal rule, the composite Simpson's 1/3 and 3/8 rules. Also, some numerical examples are presented to show the efficiency of these methods.

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Publication Date
Tue Sep 30 2008
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
COMPUTATIONAL ANALYSIS OF THE MIXING ZONE IN THE COMBUSTION CHAMBER OF RAMJET

A theoretical analysis of mixing in the secondary combustion chamber of ramjet is presented. Theoretical investigations were initiated to insight into the flow field of the mixing zone of the ramjet combustor and a computer program to calculate axisymmetric, reacting and inert flow was developed. The mathematical model of the mixing zone of ramjet comprises differential equations for: continuity, momentum, stagnation enthalpy, concentration, turbulence energy and its dissipation rate. The simultaneous solution of these equations by means of a finite-difference solution algorithm yields the values of the variable at all internal grid nodes.
The results showed that increasing air mass flow (0.32 to 0.64 kg/s) increases the development o

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Publication Date
Mon Apr 01 2019
Journal Name
2019 International Conference On Automation, Computational And Technology Management (icactm)
Multi-Resolution Hierarchical Structure for Efficient Data Aggregation and Mining of Big Data

Big data analysis is essential for modern applications in areas such as healthcare, assistive technology, intelligent transportation, environment and climate monitoring. Traditional algorithms in data mining and machine learning do not scale well with data size. Mining and learning from big data need time and memory efficient techniques, albeit the cost of possible loss in accuracy. We have developed a data aggregation structure to summarize data with large number of instances and data generated from multiple data sources. Data are aggregated at multiple resolutions and resolution provides a trade-off between efficiency and accuracy. The structure is built once, updated incrementally, and serves as a common data input for multiple mining an

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Publication Date
Mon Dec 04 2023
Journal Name
Aip Conf. Proc
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Publication Date
Wed Apr 01 2009
Journal Name
Journal Of The Faculty Of Medicine Baghdad
The Value of the chest X-Ray for diagnosing left ventricular Dysfunction

Background: The use of the chest x-ray measurements which includes the cardiothoracic ratio(C-T) and frontal area (FA) of the heart by the CXR are useful measures for primary assessment of the cardiac dysfunction.
Patients and Methods: A Prospective study was done from the 1st of January 2005 to the 1st of October in the same year on a 120 consecutive patients who have been admitted for coronary and L.V angiogram at IBN-AL-BITAR hospital. The C-T ratio and the frontal area were measured.
Results: The study comprised 120 subjects who were admitted for coronary and L.V angiogram for diagnostic reasons. 89subjects (74.2%) are male and 31subjects (25.8%) are female .17(14%) subjects have left ventricular d

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Publication Date
Mon Jun 10 2024
Journal Name
Iraqi Journal For Computer Science And Mathematics
Solving tri-criteria: total completion time, total late work, and maximum earliness by using exact, and heuristic methods on single machine scheduling problem

The presented study investigated the scheduling regarding  jobs on a single machine. Each  job will be processed with no interruptions and becomes available for the processing at time 0. The aim is finding a processing order with regard to jobs, minimizing total completion time , total late work , and maximal tardiness  which is an NP-hard problem. In the theoretical part of the present work, the mathematical formula for the examined problem will be presented, and a sub-problem of the original problem of minimizing the multi-objective functions  is introduced. Also, then the importance regarding the dominance rule (DR) that could be applied to the problem to improve good solutions will be shown. While in the practical part, two

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Publication Date
Thu Jan 11 2018
Journal Name
Al-khwarizmi Engineering Journal
The Linear and Nonlinear Electro-Mechanical Fin Actuator

Electromechanical actuators are used in a wide variety of aerospace applications such as missiles, aircrafts and spy-fly etc. In this work a linear and nonlinear fin actuator mathematical model has been developed and its response is investigated by developing an algorithm for the system using MATLAB. The algorithm used to the linear model is the state space algorithm while the algorithm used to the nonlinear model is the discrete algorithm. The huge moment constant is varied from (-3000 to 3000) and the damping ratio is varied from (0.4 to 0.8).        

 The comparison between linear and nonlinear fin actuator response results shows that for linear model, the maximum overshoot is about 10%,

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Publication Date
Tue Jan 29 2019
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Market Value Added Among Historiecal Cost and Fair Value Contravercy

Because of the vulnerability of the concept of historical cost adopted as a basis for accounting measurement to many of the criticisms in reaction counter to the concept of fair value, the aim of the research is to try to make a comparison between the historical cost and fair value to prove the health and safety of any of the measurement best for the preparation of financial statements and through the state of each of the two study secretary and good financial investment after being diagnosed with a realistic problem is the limitations of the concept of historical cost in the evaluation of assets in spite of the supposed information disclosed in the financial statements compared to appropriate property for the concept of the fair value o

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Publication Date
Thu Oct 21 2021
Journal Name
Physical Review E
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