The Splitting Crank–Nicolson Scheme with Intrinsic Parallelism for Solving Parabolic Equations

Algorithm 1

The SC-N scheme for one-dimensional parabolic equations.

	Require: Initialization U^0 (xj) ⟵ u0 (xj).
	for n = 0, 1, ⋯, N do
	for j = 0, 1, ⋯, m do
	Solve the values by using DDM I (18).
	Solve the values by using DDM II (24).
	The average of two values will be calculated, i.e. .
	end for
	end for
	Ensure: Output U^N (xj).