New Iterative Method Based on Laplace Decomposition Algorithm

Table 4

The absolute errors for Example 4.

𝑡	Exact solution	Present method
	𝑢1=𝑒^−𝑡cos(𝑡)	𝐸𝑣11	𝐸𝑣12	𝐸𝑣13
0.2	8.024106𝐸−1	1.144𝐸−2	4.432𝐸−4	1.900𝐸−5
0.4	6.174056𝐸−1	4.990𝐸−2	4.274𝐸−3	3.656𝐸−4
0.6	4.529538𝐸−1	4.185𝐸−1	1.643𝐸−2	2.119𝐸−3
0.8	3.130505𝐸−1	2.171𝐸−1	4.274𝐸−2	7.420𝐸−3
1.0	1.987661𝐸−1	3.437𝐸−1	8.925𝐸−2	1.960𝐸−2
	𝑢2=sin(𝑡)	𝐸𝑣21	𝐸𝑣22	𝐸𝑣23
0.2	1.986693𝐸−1	2.273𝐸−2	5.174𝐸−4	1.670𝐸−5
0.4	3.894183𝐸−1	1.024𝐸−1	5.840𝐸−3	1.790𝐸−4
0.6	5.646425𝐸−1	2.575𝐸−1	2.630𝐸−2	3.282𝐸−4
0.8	7.173561𝐸−1	5.082𝐸−1	8.022𝐸−2	1.276𝐸−3
1.0	8.414710𝐸−1	8.768𝐸−1	1.965𝐸−1	1.015𝐸−2