On a New Reliable Algorithm

Table 1

The absolute error from the MSHAM0.001 and RK40.001 for Case 2 of the prey-predator problem.

𝑡	Δ𝑥	Δ𝑦
2	5.7𝑒-19	8.706789680𝑒-11
4	2𝑒-20	1.178335759𝑒-11
6	1𝑒-20	1.59470390𝑒-12
8	1𝑒-20	2.1581968𝑒-13
10	2𝑒-20	2.920801𝑒-14
12	2𝑒-20	3.95288𝑒-15
14	3𝑒-20	5.3496𝑒-16
16	3𝑒-20	7.240𝑒-17
18	4𝑒-20	9.80𝑒-18
20	5𝑒-20	1.33𝑒-18