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Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method

机译：用再现核希尔伯特空间方法求解模糊微分方程的数值解

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摘要

Modeling of uncertainty differential equations is very important issue in applied sciences and engineering, while the natural way to model such dynamical systems is to use fuzzy differential equations. In this paper, we present a new method for solving fuzzy differential equations based on the reproducing kernel theory under strongly generalized differentiability. The analytic and approximate solutions are given with series form in terms of their parametric form in the space The method used in this paper has several advantages; first, it is of global nature in terms of the solutions obtained as well as its ability to solve other mathematical, physical, and engineering problems; second, it is accurate, needs less effort to achieve the results, and is developed especially for the nonlinear cases; third, in the proposed method, it is possible to pick any point in the interval of integration and as well the approximate solutions and their derivatives will be applicable; fourth, the method does not require discretization of the variables, and it is not effected by computation round off errors and one is not faced with necessity of large computer memory and time. Results presented in this paper show potentiality, generality, and superiority of our method as compared with other well-known methods.
机译：在应用科学和工程中，不确定性微分方程的建模是非常重要的问题，而对此类动力学系统进行建模的自然方法是使用模糊微分方程。在本文中，我们提出了一种在强广义可微性的基础上，基于重现核理论求解模糊微分方程的新方法。根据空间中的参数形式，以级数形式给出解析解和近似解。首先，就获得的解决方案及其解决其他数学，物理和工程问题的能力而言，它具有全球性。其次，它是准确的，需要较少的精力来获得结果，并且特别针对非线性情况而开发。第三，在所提出的方法中，可以在积分区间内选择任意点，并且近似解及其导数将适用。第四，该方法不需要离散化变量，并且不受计算舍入误差的影响，并且不需要面对大计算机存储器和时间的需求。本文介绍的结果表明，与其他知名方法相比，我们的方法具有潜力，通用性和优越性。

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