Numerical solution of bipolar fuzzy initial value problem

Differential equations occur in many fields of science, engineering and social science as it is a natural way of modeling uncertain dynamical systems. A bipolar fuzzy set model is useful mathematical tool for addressing uncertainty which is an extension of fuzzy set model. In this paper, we study differential equations in bipolar fuzzy environment. We introduce the concept gH-derivative of bipolar fuzzy valued function. We present some properties of gH-differentiability of bipolar fuzzy valued function by considering different types of differentiability. We consider bipolar fuzzy Taylor expansion. By using Taylor expansion, Euler method is presented for solving bipolar fuzzy initial value problems. We discuss convergence analysis of proposed method. We describe some numerical examples to see the convergence and stability of the method and compute global truncation error. From numerical results, we see that for small step size Euler method converges to exact solution.