### Table 3: The percentages of the stable solutions implicit semi-implicit composite

"... In PAGE 11: ...5 convergence property of the iterative method for the nonlinear equation are all good in this step. In Table3 , we give percentages of stable solutions obtained by the implicit Euler method, the semi-implicit Euler method and the composite Euler method, respectively. All of the data about percentages of stable solutions are based on 5000 simulated trajectories.... ..."

### Table 1: Maximum error in the energy using the semi-implicit method with the energy conserving method (6) for the strong forces.

1997

"... In PAGE 13: ...Table1 for various values of k, , and . Even for large and , the value of H depends quadratically on the step size k, which seems to indicate that our semi-implicit method behaves like a second order method in the slow variables, at least for this example.... In PAGE 13: ... However, these two methods remain close. Repeating the experi- ments of Table1 produces qualitatively similar results for the Morse potential. The computations with either (6) or (7) are stable.... ..."

Cited by 7

### Table 2: Transformed coe cient matrices for semi-implicit Crank-Nicolson method.

1994

"... In PAGE 15: ...Table 2: Transformed coe cient matrices for semi-implicit Crank-Nicolson method. Table2 shows the structure for each combination of P1i, P1e and P2 with Q1i and Q1e. The relative merits of each transformation are di cult to judge; we will only attempt a super cial analysis here.... ..."

Cited by 2

### Table 1. Maximum error in the energy using the semi-implicit method with the energy conserving method (6) for the strong forces.

1997

"... In PAGE 13: ...13 can be found in Table1 for various values of k, , and . Even for large and , the value of H depends quadratically on the step size k.... In PAGE 13: ... However, these two methods remain close. Repeating the experiments of Table1 produces qualitatively similar results for the Morse potential. The computations with either (6) or (7) are stable.... ..."

Cited by 7

### Table 1. Maximum error in the energy using the semi-implicit method with the energy conserving method (6) for the strong forces.

1997

"... In PAGE 13: ...13 can be found in Table1 for various values of k, , and . Even for large and , the value of H depends quadratically on the step size k.... In PAGE 13: ... However, these two methods remain close. Repeating the experiments of Table1 produces qualitatively similar results for the Morse potential. The computations with either (6) or (7) are stable.... ..."

Cited by 7

### Table, Chair, and Bed) only know this information semi-implicitly. The behavior of retrieving local and world transforms is best described inductively:

2004

Cited by 31

### Table, Chair, and Bed) only know this information semi-implicitly. The behavior of retrieving local and world transforms is best described inductively:

Cited by 6

### Table 5: Price/performance comparison for di erent systems. Performance is measured as the total elapsed time (in sec) to complete a 6-hour production run for a 128 128 16 grid with the semi-implicit version of the HIRLAM forecast model.

### Table 6: Extra times for executing one time step using the semi-Lagrangian formulation with the di erent implementations of the interpolation routine in the spectral semi-implicit HIRLAM fore- cast model with a 110 100 16 integration area on a MasPar MP-2 with 16K processors. Also the total execution time for one time step in the spectral semi-implicit Eulerian formulation is shown. Implementation Time (in sec)

### Table 6.2: Comparison between ESIRK, SIRK and ERK. In Fig.6.2 we plot the CPU-time as a function of log Re. As expected more or less Re-independent convergence is obtained by SIRK and ESIRK, whereas the number of iterations increases as Re1=2 for ERK. Clearly the semi-implicit schemes are much better suited than the explicit scheme for high Re.

1995

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