A local fractional modified Crank–Nicolson scheme for fractal LWR model of traffic flow

Abstract

This research proposes a modified Crank–Nicolson finite difference scheme with local fractional derivatives to approximate the solutions of local fractional LWR traffic flow model. The stability and consistency of the scheme are examined. Further, convergence of the scheme is assured by using Lax’s equivalence theorem. Some exemplary instances are discussed along with their simulations to validate the proposed method. The obtained numerical solutions show the dynamical evolution of traffic density with respect to time and space. The results derived using the proposed numerical scheme establish that they are quite effective in obtaining the numerical solution to the fractal vehicular traffic flow problem.