论文标题
使用分数迭代方法降低非线性系统及其数值解决方案
Reduction of a nonlinear system and its numerical solution using a fractional iterative method
论文作者
论文摘要
5个变量的非线性代数方程系统是数值求解的，该方程是从傅立叶变换到微分方程系统的应用中得出的，该方程式允许建模温度的行为以及混合太阳接收机的效率，这简单地是简单的术语，即在热电器系统中的组合。另外，提出了一种将先前系统减少到仅2个变量的非线性系统的方法。自然地，将尺寸n的代数方程式降低到较小维度的系统的主要优点是减少问题中涉及的变量数量，但是系统的分析表达式变得更加复杂。但是，为了最大程度地减少这种缺点，使用了一种不明确取决于要解决的系统的分析复杂性的迭代方法。一种使用分数演算的属性的一个分数迭代方法，对一个和几个变量有效，特别是，常数的分数衍生物并不总是零，以找到非线性系统的解决方案。
A nonlinear algebraic equation system of 5 variables is numerically solved, which is derived from the application of the Fourier transform to a differential equation system that allows modeling the behavior of the temperatures and the efficiencies of a hybrid solar receiver, which in simple terms is the combination of a photovoltaic system with a thermoelectric system. In addition, a way to reduce the previous system to a nonlinear system of only 2 variables is presented. Naturally, reducing algebraic equation systems of dimension N to systems of smaller dimensions has the main advantage of reducing the number of variables involved in a problem, but the analytical expressions of the systems become more complicated. However, to minimize this disadvantage, an iterative method that does not explicitly depend on the analytical complexity of the system to be solved is used. A fractional iterative method, valid for one and several variables, that uses the properties of fractional calculus, in particular the fact that the fractional derivatives of constants are not always zero, to find solutions of nonlinear systems is presented.
