Improved Milne-Hamming Method for Resolving High-Order Uncertain Differential Equations

Abstract

Uncertain systems can be modeled using high-order uncertain differential equations, however, which are often difficult to resolve via analytical methods, so what’s necessary is how to devise a numerical method. Based on the Milne-Hamming formula, this paper presented a new numerical solution—improved Milne-Hamming method. It showed that improved Milne-Hamming method is better than other numerical methods through numerical experiments. In addition, the analysis of its convergence, stability, and time complexity was given. After this, this method was implemented to acquire the expected value, extreme value, and integral of the solution. Finally, a concise conclusion was obtained.