  A method for enhancing the stability and robustness of explicit schemes in
computational fluid dynamics is presented. The method is based in reformulating
explicit schemes in matrix form, which cane modified gradually into semi or
strongly-implicit schemes. From the point of view of matrix-algebra, explicit
numerical methods are special cases in which the global matrix of coefficients
is reduced to the identity matrix $I$. This extreme simplification leads to
severer stability range, hence of their robustness. In this paper it is shown
that a condition, which is similar to the Courant-Friedrich-Levy (CFL)
condition can be obtained from the stability requirement of inversion of the
coefficient matrix. This condition is shown to be relax-able, and that a class
of methods that range from explicit to strongly implicit methods can be
constructed, whose degree of implicitness depends on the number of coefficients
used in constructing the corresponding coefficient-matrices. Special attention
is given to a simple and tractable semi-explicit method, which is obtained by
modifying the coefficient matrix from the identity matrix $I$ into a
diagonal-matrix $D$. This method is shown to be stable, robust and it can be
applied to search for stationary solutions using large CFL-numbers, though it
converges slower than its implicit counterpart. Moreover, the method can be
applied to follow the evolution of strongly time-dependent flows, though it is
not as efficient as normal explicit methods. In addition, we find that the
residual smoothing method accelerates convergene toward steady state solutions
considerably and improves the efficiency of the solution procedure.
