A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain

Table 1

Numerical results of Example 13, for Re(exp(𝑧))=exp(𝑥)cos(𝑦).

𝑧=𝑥+𝑖𝑦	Exact solution (real)	PM for 𝑁=5	PM for 𝑁=7	PM for 𝑁=9
0.0+0.0𝑖	1.000000000000000	1.000000000000002	0.999999999999999	1.000000000000002
0.1+0.1𝑖	1.099649666829409	1.099650127059032	1.099649681790901	1.099649666809790
0.2+0.2𝑖	1.197056021355891	1.197058065414137	1.197056071303251	1.197056021305326
0.3+0.3𝑖	1.289569374044936	1.289572683703872	1.289569451705194	1.289569373971185
0.4+0.4𝑖	1.374061538887522	1.374064757066184	1.374061646628469	1.374061538795035
0.5+0.5𝑖	1.446889036584169	1.446891795476775	1.446889179088898	1.446889036484456
0.6+0.6𝑖	1.503859540558786	1.503862872087464	1.503859710928599	1.503859540462517
0.7+0.7𝑖	1.540203025431780	1.540203451564549	1.540203240474244	1.540203025363573
0.8+0.8𝑖	1.550549296807422	1.550520218427163	1.550549536105736	1.550549296761452
0.9+0.9𝑖	1.528913811884699	1.528765905385641	1.528913283429636	1.528913812578978
1.0+1.0𝑖	1.468693939915885	1.468204121679876	1.468688423751699	1.468693951050675