Improved Finite Difference Technique via Adomian Polynomial to Solve the Coupled Drinfeld’s–Sokolov–Wilson System

Algorithm 2

Algorithm of the EFD-AP method.

	Input: the values of a, , , and confections , number of space fragmentation , and for time
	Step 1: evaluate space step size and time step size.
	Step 2: find the values of α = T/2H, β = , and µ =
	Step 3: compute the initial condition and boundary conditions
	, ,
	,
	, , .
	Step 4: calculate the Adomian polynomials
	Step 5: compute the numerical solution from
	.
	where j = 1, 2, …, m − 1, and i = 1, 2, …, n − 1
	compute the numerical solution at i = 1 from
	and the numerical solution at i = n − 1 from
	.
	Step 6: when i = 2, 3, …, n − 2, compute the numerical solution from .
	Step 7: print the numerical solutions u(x, t) and (x, t).