The primary objective of the current paper is to suggest and implement effective computational methods (DECMs) to calculate analytic and approximate solutions to the nonlocal one-dimensional parabolic equation which is utilized to model specific real-world applications. The powerful and elegant methods that are used orthogonal basis functions to describe the solution as a double power series have been developed, namely the Bernstein, Legendre, Chebyshev, Hermite, and Bernoulli polynomials. Hence, a specified partial differential equation is reduced to a system of linear algebraic equations that can be solved by using Mathematica®12. The techniques of effective computational methods (DECMs) have been applied to solve some specific cases of time-dependent diffusion equations. Moreover, the maximum absolute error () is determined to demonstrate the accuracy of the proposed techniques.
A new ligand complexes have been synthesis from reaction of metal ions of Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II), Hg(II), Pd(II) and Pt(II) with schiff base LH. 5-[(2-Hydroxy-naphthalen-1-ylmethylene)-amino]-2-phenyl-2,4-dihydro-pyrazol-3-one, this ligand was characterized by Fourier transform infrared (FTIR), UV-vis, 1H, 13CNMR, and mass spectra. All complexes were characterized by techniques micro analysis C.H.N, UV-vis and FTIR spectral studies, atomic absorption, chloride content, molar conductivity measurements and magnetic susceptibility. The ligand acts as bidentate, coordination through nitrogen atom from azomethin group and deprotonated phenolic oxygen atom. The spectroscopic and analytical measurements showed that
... Show MoreThis research a study model of linear regression problem of autocorrelation of random error is spread when a normal distribution as used in linear regression analysis for relationship between variables and through this relationship can predict the value of a variable with the values of other variables, and was comparing methods (method of least squares, method of the average un-weighted, Thiel method and Laplace method) using the mean square error (MSE) boxes and simulation and the study included fore sizes of samples (15, 30, 60, 100). The results showed that the least-squares method is best, applying the fore methods of buckwheat production data and the cultivated area of the provinces of Iraq for years (2010), (2011), (2012),
... Show MoreAlgorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.
The aim of this paper is to propose a reliable iterative method for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method. Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibits that this technique was compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.
In this paper, a method based on modified adomian decomposition method for solving Seventh order integro-differential equations (MADM). The distinctive feature of the method is that it can be used to find the analytic solution without transformation of boundary value problems. To test the efficiency of the method presented two examples are solved by proposed method.
Scheduling Timetables for courses in the big departments in the universities is a very hard problem and is often be solved by many previous works although results are partially optimal. This work implements the principle of an evolutionary algorithm by using genetic theories to solve the timetabling problem to get a random and full optimal timetable with the ability to generate a multi-solution timetable for each stage in the collage. The major idea is to generate course timetables automatically while discovering the area of constraints to get an optimal and flexible schedule with no redundancy through the change of a viable course timetable. The main contribution in this work is indicated by increasing the flexibility of generating opti
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