Adaptive Numerical Method for Approximation of Traffic Flow Equations

Table 1

A comparison of the solution of equation of example 1 using the present method with other numerical methods.

t	x	Without MLS	Mathematica	New method
5	−20	0.2624	0.2640	0.2631
	−10	0.6136	0.5600	0.5613
	0	0.8872	0.9089	0.9184
	10	0.4653	0.4695	0.4726
	20	0.2618	0.2624	0.2626
10	−20	0.2628	……	0.2633
	−10	0.7288	……	0.6537
	0	0.8877	……	0.8535
	10	0.4334	……	0.4476
	20	0.2616	……	0.2625
15	−20	0.2632	……	0.2636
	−10	0.8444	……	0.8151
	0	0.7369	……	0.7877
	10	0.4112	……	0.4285
	20	0.2615	……	0.2623
20	−20	0.2599	……	0.2639
	−10	0.9019	……	0.9347
	0	0.7410	……	0.7313
	10	0.3976	……	0.4134
	20	0.2621	……	0.2622
25	−20	0.2538	……	0.2646
	−10	0.8550	……	0.9388
	0	0.5769	……	0.6844
	10	0.3849	……	0.4016
	20	0.2606	……	0.2620