Nonlinear Klein-Gordon and Schrödinger Equations by the Projected Differential Transform Method

Table 4

Comparison for the absolute errors |𝐸𝑣| and |𝐸𝑤| of the approximate solutions obtained by SCMP, DTM, and PDTM at various test point 𝑥_𝑖 with fixed time 𝑡=1.

𝑥	|𝐸𝑣(𝑥𝑖,0)|
	SCMP	DTM	PDTM
𝑥3	1.3281×10^−9	1.5029×10^−3	1.5739×10^−11
𝑥7	2.2164×10^−9	1.1175×10^−6	1.7926×10^−11
𝑥11	2.2164×10^−9	3.0748×10^−11	3.0690×10^−11
𝑥14	2.3774×10^−9	7.3818×10^−12	7.3817×10^−12
𝑥	|𝐸𝑤(𝑥𝑖,0)|
	SCMP	DTM	PDTM
𝑥3	9.4638×10^−10	2.1193×10^−2	1.3898×10^−12
𝑥7	4.0901×10^−10	1.5759×10^−5	1.5830×10^−12
𝑥11	4.0901×10^−10	2.7100×10^−12	2.7101×10^−12
𝑥14	1.4319×10^−9	6.5184×10^−13	6.5184×10^−13