The GDTM-Padé Technique for the Nonlinear Lattice Equations

Table 1

The operations for generalized differential transform method.

Original function	Transformed function
𝑓(𝑛,𝑡)=𝑔(𝑛,𝑡)+ℎ(𝑛,𝑡)	𝐹(𝑛,𝑘)=𝐺(𝑛,𝑘)+𝐻(𝑛,𝑘)
𝑓(𝑛,𝑡)=𝛼𝑔(𝑛,𝑡)	𝐹(𝑛,𝑘)=𝛼𝐺(𝑛,𝑘)
𝑓(𝑛,𝑡)=𝜕𝑔(𝑛,𝑡)/𝜕𝑡	𝐹(𝑛,𝑘)=(𝑘+1)𝐺(𝑛,𝑘+1)
𝑓(𝑛,𝑡)=𝑔(𝑛,𝑡)ℎ(𝑛,𝑡)	𝐹(𝑛,𝑘)=∑^𝑘𝑟=0𝐺(𝑛,𝑟)𝐻(𝑛,𝑘−𝑟)
𝑓(𝑛,𝑡)=𝜕^𝑚𝑔(𝑛,𝑡)/𝜕𝑡^𝑚	𝐹(𝑛,𝑘)=(𝑘+𝑚)𝐺(𝑛,𝑘+𝑚)
𝑓(𝑛,𝑡)=𝑔(𝑛+𝑠,𝑡)	𝐹(𝑛,𝑘)=𝐺(𝑛+𝑠,𝑘)