Implicit Numerical Solutions for Solving Stochastic Differential Equations with Jumps

Table 1

Mean of the absolute errors for different values of Δ and different methods.

Methods	Δ	2^−8	2^−7	2^−6	2^−5	2^−4	2^−3	2^−2	2^−1
𝜃-Taylor	𝜃=0	0.0024	0.0048	0.0099	0.0186	0.0389	0.0911	0.6853	3.0473
	𝜃=1/2	0.0022	0.0043	0.0090	0.0177	0.0368	0.0805	0.2548	0.7407
	𝜃=1	0.0042	0.0083	0.0170	0.0342	0.0699	0.1454	0.3025	0.5568
Balanced 𝜃-Taylor	𝜃=0	0.0021	0.0041	0.0083	0.0152	0.0317	0.0665	0.3852	1.5570
	𝜃=1/2	0.0076	0.0134	0.0223	0.0361	0.0619	0.1504	0.7024	3.1984
	𝜃=1	0.0075	0.0132	0.0217	0.0347	0.0582	0.1360	0.6285	2.6648