A LOCAL FRACTIONAL NON-STANDARD FINITE DIFFERENCE SCHEME FOR FRACTAL LWR MODEL OF TRAFFIC FLOW

A LOCAL FRACTIONAL NON-STANDARD FINITE DIFFERENCE SCHEME FOR FRACTAL LWR MODEL OF TRAFFIC FLOW

B. Pokhriyal, P. Goswami, K. Kumar

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Abstract

In this paper, a non-standard local fractional Crank-Nicolson finite difference scheme is proposed to determine an approximation to the solutions of the fractal LWR traffic flow model. The scheme is found to be consistent and unconditionally stable. In addition, Lax’s equivalence theorem is used to guarantee the scheme’s convergence. The suggested approach is validated by discussing a few exemplary cases and associated simulations. The acquired numerical solutions demonstrate how traffic density changes dynamically across time and space. The outcomes obtained with the suggested nonstandard finite difference (NSFD) method demonstrate its effectiveness in numerically solving the problem of fractal traffic flow.

Keywords

Local fractional calculus, numerical scheme, non-standard finite difference scheme, Crank-Nicolson method, traffic flow model.