In many fields of science, engineering and social sciences, fuzzy differential equations occur as it is the simplest way to model unpredictable dynamical systems. In many contexts and scientific disciplines, certain aspects of uncertainty in data are likely to occur. In applied fields, various types of vagueness were recognized. Some are caused by incomplete or contradictory information, as well as different interpretations of the same phenomenon. In various applications like belief systems, expert systems, and information fusion, one real value from the interval [0, 1] in favor of a certain property can not be utilized conveniently, as it is much useful to consider its counter-property. Many domains have bipolarity as a central characteristic. This paper deals with bipolar fuzzy initial value problems (BFIVPs). Numerical methods have much importance because we have many problems which cannot be solved analytically or it is much complicated to solve them analytically. We introduce a Runge–Kutta method to solve BFIVPs. To check efficiency and validity of proposed method, we prove the consistency, convergence and stability of the method. The proposed method is simple to implement as it does not require higher order derivatives of function. The local truncation errors of Euler and Modified Euler methods are \(O(h^{2})\) and \(O(h^{3})\), respectively, while local truncation errors in proposed Runge–Kutta method is \(O(h^{5})\). We apply an introduced method to solve a few numerical examples. We give the comparison of our proposed method with the Euler and Modified Euler methods by finding global truncation errors. Numerical results show the acceptable accuracy of proposed method.

在科学，工程学和社会科学的许多领域中，出现模糊微分方程是因为它是对不可预测的动力学系统建模的最简单方法。在许多情况下和科学学科中，数据不确定性的某些方面可能会发生。在应用领域，人们认识到各种类型的模糊性。有些是由于信息不完整或矛盾以及对同一现象的不同解释造成的。在诸如信念系统，专家系统和信息融合之类的各种应用中，不能方便地利用来自间隔[0，1]的支持某个特性的一个实际值，因为考虑其反特性非常有用。许多领域都以双极性为中心特征。本文讨论双极性模糊初值问题（BFIVP）。数值方法非常重要，因为我们有许多无法解析解决的问题，或者解析起来很难解决的问题。我们介绍了一种Runge–Kutta方法来求解BFIVP。为了检验所提方法的有效性和有效性，我们证明了该方法的一致性，收敛性和稳定性。所提出的方法易于实现，因为它不需要函数的高阶导数。欧拉方法和改进的欧拉方法的局部截断误差为 所提出的方法易于实现，因为它不需要函数的高阶导数。欧拉方法和修正欧拉方法的局部截断误差为 所提出的方法易于实现，因为它不需要函数的高阶导数。欧拉方法和改进的欧拉方法的局部截断误差为\（O（h ^ {2}）\）和\（O（h ^ {3}）\），而建议的Runge–Kutta方法中的局部截断错误为\（O（h ^ {5}）\ ）。我们采用一种介绍的方法来解决一些数值示例。通过找到全局截断误差，我们将我们提出的方法与Euler方法和Modified Euler方法进行了比较。数值结果表明了所提方法的准确性。