Numerical Solution and Simulation of Second-Order Parabolic PDEs with Sinc-Galerkin Method Using Maple

Table 1

Conformal mappings and nodes for several subintervals of 𝑅.

(𝑎,𝑏)		ϕ (𝑧)	𝑧𝑘
𝑎	𝑏	ln𝑧−𝑎𝑏−𝑧	𝑎+𝑏𝑒^𝑘ℎ1+𝑒^𝑘ℎ
0	1	𝑧ln1−𝑧	𝑒^𝑘ℎ1+𝑒^𝑘ℎ
0	∞	ln(𝑧)	𝑒^𝑘ℎ
0	∞	ln(sinh(𝑧))	ln𝑒^𝑘ℎ+𝑒^2𝑘ℎ+1
−∞	∞	𝑧	𝑘ℎ
−∞	∞	sinh^−1(𝑧)	𝑘ℎ