Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method

Table 1

Evaluation of numerical errors for 𝑁=4.

𝑥	𝑌	𝑢(𝑥,𝑦) exact	𝑢(𝑥,𝑦)  𝑁=4	Error
0.25	0.25	−0.0253303	−0.0253303	6.27007⋅10^−11
	0.5	−0.0358224	−0.0358224	8.86722⋅10^−11
	0.75	−0.0253303	−0.0253303	6.27007⋅10^−11
	0.95	−0.00560387	−0.00560387	1.38714⋅10^−11
0.5	0.25	−0.0358224	−0.0358224	1.26904⋅10^−11
	0.5	−0.0506606	−0.0506604	1.79469⋅10^−7
	0.75	−0.0358224	−0.0358223	1.26904⋅10^−11
	0.95	−0.00792506	−0.00792506	2.80752⋅10^−8
0.75	0.25	−0.0253303	−0.0253195	1.07646⋅10^−5
	0.5	−0.0358224	−0.0358072	1.52235⋅10^−5
	0.75	−0.0253303	−0.0253195	1.07646⋅10^−5
	0.95	−0.00560387	−0.00560148	2.38148⋅10^−6
0.95	0.25	−0.00560387	−0.00546191	0.000141956
	0.5	−0.00792506	−0.00772431	000200756
	0.75	−0.00560387	−0.00546191	0.000141956
	0.95	−0.00123975	−0.00120835	3.14051⋅10^−5