Stabilized fourth order extended methods for the numerical solution of odes

Non-dissipative extended one-step methods for oscillatory problems

“…Since the phase-lag for these methods is independent of the free parameter 720, for reasons explained in Chawla et al [5], a "best" choice for this parameter is y2, = 2. The resulting fourth order non-dissipative extended one-step method is displayed in the following table.…”

Optimal extended one-step schemes of exponential type for stiff initial-value problems

“…We now verify that the schemes (5), (14) and (27) (14) and (27). Then, at each mesh point x j , we have the following error estimate:…”

“…(5) and (14) and (6) with m = 3. One can verify that the coefficients (28) satisfy the conditions (13) and (16) with m = 3.…”

“…(14) and the coefficients q −1 , q 0 and q 1 are defined in the form (6) with m = 2. Similar to that mentioned earlier, we can compute the present schemes with m = 3.…”

“…Kondrat and Jacques [13] gave extended two-step fourth order A-stable methods. Chawla et al [14] described fourth order extended one-step methods, which are A-and/or L-stable. Chawla et al [15] derived fifth order extended one-step methods, which are A-and/or L-stable.…”