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A semi-analytical iterative technique for solving chemistry problems

机译：一种解决化学问题的半解析迭代技术

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The main aim and contribution of the current paper is to implement a semi-analytical iterative method suggested by Temimi and Ansari in 2011 namely (TAM) to solve two chemical problems. An approximate solution obtained by the TAM provides fast convergence. The current chemical problems are the absorption of carbon dioxide into phenyl glycidyl ether and the other system is a chemical kinetics problem. These problems are represented by systems of nonlinear ordinary differential equations that contain boundary conditions and initial conditions. Error analysis of the approximate solutions is studied using the error remainder and the maximal error remainder. Exponential rate for the convergence is observed. For both problems the results of the TAM are compared with other results obtained by previous methods available in the literature. The results demonstrate that the method has many merits such as being derivative-free, and overcoming the difficulty arising in calculating Adomian polynomials to handle the non-linear terms in Adomian Decomposition Method (ADM). It does not require to calculate Lagrange multiplier in Variational Iteration Method (VIM) in which the terms of the sequence become complex after several iterations, thus, analytical evaluation of terms becomes very difficult or impossible in VIM. No need to construct a homotopy in Homotopy Perturbation Method (HPM) and solve the corresponding algebraic equations. The MATHEMATICA? 9 software was used to evaluate terms in the iterative process.
机译：本文的主要目的和贡献是实现了Temimi和Ansari在2011年提出的半分析迭代方法（TAM），以解决两个化学问题。通过TAM获得的近似解决方案可提供快速收敛。当前的化学问题是二氧化碳吸收到苯基缩水甘油醚中，而另一个系统是化学动力学问题。这些问题由包含边界条件和初始条件的非线性常微分方程组表示。使用误差余数和最大误差余数研究近似解的误差分析。观察到收敛的指数速率。对于这两个问题，将TAM的结果与通过文献中现有方法获得的其他结果进行比较。结果表明，该方法具有无导数等优点，克服了Adomian分解法计算Adomian多项式来处理非线性项的困难。不需要使用变分迭代法（VIM）来计算拉格朗日乘数，在变分迭代法（VIM）中，序列的项经过几次迭代后变得复杂，因此，在VIM中对项的分析评估变得非常困难或不可能。无需在同伦摄动法（Homopypy Perturbation Method，HPM）中构造同伦，并求解相应的代数方程。 MATHEMATICA？使用9个软件评估迭代过程中的术语。

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