Z+-Initial Value Problem with Extended Triangular Distribution

Z-differential equations are used to model phenomena under uncertainty and partial reliability in scientific and engineering fields. Most existing methods for z-differential equations that involve z-numbers are based on discrete forms; however, the continuous form of z-numbers is more representative of the behavior of many phenomena. In this work, we examine z+-numbers with triangular distributions as initial conditions in uncertain differential equations. The numerical method, called the Modified Euler method, is generalized to solve z+-initial value problems, with proofs provided for its convergence and stability. Several examples are provided to demonstrate the accuracy and efficiency of the proposed method.