Nonstandard finite difference scheme for a Tacoma Narrows Bridge model

Abstract

• Two nonstandard finite difference (NSFD) schemes for a system of ODEs are proposed. • These difference schemes follow the Mickens methodology for constructing NSFD schemes. • NSFD schemes shown to give better numerical solutions to the nonlinear ODEs. This paper constructs two dynamically consistent nonstandard finite difference (NSFD) schemes for the model of Tacoma Narrows Bridge using the Mickens methodology. The model consists of nonlinear, coupled, second order ordinary differential equations (ODEs). The standard forward Euler fails to capture the correct behavior of the system for a given step size. However, using the same step size, both NSFD schemes correctly approximate the solution to the system.