Solving High-Order Uncertain Differential Equations Via Adams-Simpson Method

High-order uncertain differential equations are a type of differential equations involving the high-order derivatives of uncertain processes and are widely used in modeling differentiable uncertain systems with high-order differentials.Because the analytical solutions of general high-order uncertain differential equations have complex forms or do not exist at all,how to design numerical methods to solve high-order uncertain differential equations has always been a core issue.Essentially,a multidimensional uncertain differential equation is a system.In fact,high-order uncertain differential equations can be transformed into multi-dimensional uncertain differential equations.Through the Yao formula,the solutions of high-order uncertain differential equations can be represented by a set of solutions of corresponding high-order ordinary differential equations.Based on this,an efficient numerical method can be designed to solve the numerical solution of high-order uncertain differential equations.This paper proposes a new numerical method-Adams-Simpson method to solve highorder uncertain differential equations,and through numerical experiments to further compare and study the efficiency of the Adams-Simpson method to solve high-order uncertain differential equations compared to Runge-Kutta method.At the same time,the convergence,stability and time complexity of the Adams-Simpson numerical method are analyzed and explored.Furthermore,this paper gives how to calculate the expected value,the inverse uncertainty distributions of the extreme value and the integral of the solution of the high-order uncertain differential equation with the aid of Ada.ms-Simpson method.