The RELAP5 transient thermal-hydraulic code is a widely accepted analysis tool for light water nuclear reactor safety studies. There are several matrix solvers in the code that can consume a significant portion of run time. Enhancing the diagonal dominance of the coefficient matrix used in the matrix solver for the nearly implicit method can significantly improve the code performance. Three numerical schemes are presented for enhancing the diagonal dominance of the coefficient matrix, and it is shown that for all three schemes the same solution strategy can be repeated from one time level to another. These schemes, therefore, give grind times that can be considerably smaller than the scheme originally used in the code. Numerical results confirm the findings.