The Numerical Solution of Singularly Perturbed Nonlinear Partial Differential Equations in Three Space Variables: The Adaptive Explicit Inverse Preconditioning Approach

Algorithm 1

mEPCG ().

	Purpose: a modified PCG method is used for solving a given system of linear equations
	Input: A is a symmetric and positive definite coefficient matrix, b is the right-hand side vector, tol is the predermined tolerance, is the initial guess, is a SP-inverse parameter, and is the required inverse preconditioner
	Output: x the solution vector.
	Computational Procedure
	Step 1: given , εP SP-inverse parameter, inverse preconditioner
	Step 2: set
	Step 3: solve , for y0
	Step 4: set
	Step 5: while
	Step 6: compute a step length
	Step 7: update the approximate solution
	Step 8: update the residual
	Step 9: solve
	Step 10: compute a gradient correction factor
	Step 11: set the new search direction
	Step 12:
	Step 13: end (while)