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حل المعادلات التفاضلية الجزئية باستخدام طريقة الشبكة العددية

1747   2   2   0.0 ( 0 )
 Publication date 2018
  fields Mathematics
and research's language is العربية
 Created by Shamra Editor




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References used
Hockney, R.W., East wood,J.E, Computer simulation using particles, Mc Graw-Hill, , 1987
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In this article, powerful approximate analytical methods, called Adomian decomposition method and variational iteration method are introduced and applied to obtaining the approximate analytical solutions for an important models of linear and non- linear partial differential equations such as ( nonlinear Klein Gordon equation - nonlinear wave equation - linear telegraph equation - nonlinear diffusion convection equation ) . The studied examples are used to reveal that those methods are very effective and convenient for solving linear and nonlinear partial differential equations . Numerical results and comparisons with the exact solution are included to show validity, ability, accuracy, strength and effectiveness of those techniques.
In this paper, we introduce a numerical method for solving systems of high-index differential algebraic equations. This method is based on approximating the exact solution by spline polynomial of degree eight with five collocation points to find the numerical solution in each step. The study shows that the method when applied to linear differential-algebraic systems with index equal one is stable and convergent of order 8, while it is stable and convergent of order 9-u for index equal u . Numerical experiments for four test examples and comparisons with other available results are given to illustrate the applicability and efficiency of the presented method
Machine learning methods for financial document analysis have been focusing mainly on the textual part. However, the numerical parts of these documents are also rich in information content. In order to further analyze the financial text, we should as say the numeric information in depth. In light of this, the purpose of this research is to identify the linking between the target cashtag and the target numeral in financial tweets, which is more challenging than analyzing news and official documents. In this research, we developed a multi model fusion approach which integrates Bidirectional Encoder Representations from Transformers (BERT) and Convolutional Neural Network (CNN). We also encode dependency information behind text into the model to derive semantic latent features. The experimental results show that our model can achieve remarkable performance and outperform comparisons.

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