Numerical Solutions of a Variable-Order Fractional Financial System

Table 1

Maximum error and convergent order of Example 4.1 with different step sizes (computed once via the Adams-Bashforth-Moulton method).

Nodes	Step sizes	Maximum error	Convergent order 𝛼
10	ℎ=0.10	0.06266509659082	1.203
20	ℎ=0.05	0.03020056515385	1.168
50	ℎ=0.02	0.01002178106628	1.177
100	ℎ=0.01	0.00329319942345	1.241

Note: when estimating the convergent order, we employ formula 𝛼=log(maximumerror)/log(stepsize). The theoretical convergent order provided by (3.7) is 1.667. We take the numerical solution with step size ℎ=0.005 as the exact results.