An Efficient Spectral Approximation for Solving Several Types of Parabolic PDEs with Nonlocal Boundary Conditions

Table 1

Error |𝑒₈(𝑥,𝑡)|(=|𝑢(𝑥,𝑡)−𝑢₈(𝑥,𝑡)|) comparison of the PM and BTM for Example 1.

(𝑥,𝑡)	PM	BTM
(0,0)	3.86722𝑒−029	1.31773𝑒−007
(0.1,0.1)	2.31062𝑒−006	7.87467𝑒−005
(0.2,0.2)	2.52185𝑒−006	2.05301𝑒−004
(0.3,0.3)	2.87530𝑒−006	3.11401𝑒−004
(0.4,0.4)	3.20632𝑒−006	3.78699𝑒−004
(0.5,0.5)	3.56079𝑒−006	4.02938𝑒−005
(0.6,0.6)	3.97452𝑒−006	3.84876𝑒−004
(0.7,0.7)	4.46780𝑒−006	3.28180𝑒−004
(0.8,0.8)	5.01629𝑒−006	2.38398𝑒−004
(0.9,0.9)	6.08046𝑒−006	1.25456𝑒−004
(1.0,1.0)	7.63453𝑒−030	1.31773𝑒−007