𝑃-stable Obrechkoff methods with minimal phase-lag for periodic initial value problems

Anantha Krishnaiah, U.

doi:10.1090/S0025-5718-1987-0906188-X

$P$-stable Obrechkoff methods with minimal phase-lag for periodic initial value problems
HTML articles powered by AMS MathViewer

by U. Anantha Krishnaiah PDF

Math. Comp. 49 (1987), 553-559 Request permission

Abstract:

In this paper P-stable methods of $O({h^6})$ and $O({h^8})$ with minimal phase-lag (frequency distortion) are derived. Numerical results for both linear and nonlinear problems are presented.

References

U. Anantha Krishnaiah, A class of two-step P-stable methods for the accurate integration of second order periodic initial value problems, J. Comput. Appl. Math. 14 (1986), no. 3, 455–459. MR 831087, DOI 10.1016/0377-0427(86)90080-4

Internat. J. Numer. Methods Engrg.

J. R. Cash, High order $P$-stable formulae for the numerical integration of periodic initial value problems, Numer. Math. 37 (1981), no. 3, 355–370. MR 627110, DOI 10.1007/BF01400315
M. M. Chawla, Two-step fourth order $P$-stable methods for second order differential equations, BIT 21 (1981), no. 2, 190–193. MR 627879, DOI 10.1007/BF01933163
M. M. Chawla and P. S. Rao, A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems, J. Comput. Appl. Math. 11 (1984), no. 3, 277–281. MR 777103, DOI 10.1016/0377-0427(84)90002-5
Germund Dahlquist, On accuracy and unconditional stability of linear multistep methods for second order differential equations, BIT 18 (1978), no. 2, 133–136. MR 499228, DOI 10.1007/BF01931689
Walter Gautschi, Numerical integration of ordinary differential equations based on trigonometric polynomials, Numer. Math. 3 (1961), 381–397. MR 138200, DOI 10.1007/BF01386037
I. Gladwell and R. M. Thomas, Damping and phase analysis for some methods for solving second-order ordinary differential equations, Internat. J. Numer. Methods Engrg. 19 (1983), no. 4, 495–503. MR 702055, DOI 10.1002/nme.1620190404
E. Hairer, Unconditionally stable methods for second order differential equations, Numer. Math. 32 (1979), no. 4, 373–379. MR 542200, DOI 10.1007/BF01401041
M. K. Jain, R. K. Jain, and U. Anantha Krishnaiah, $P$-stable methods for periodic initial value problems of second order differential equations, BIT 19 (1979), no. 3, 347–355. MR 548614, DOI 10.1007/BF01930988
J. D. Lambert and I. A. Watson, Symmetric multistep methods for periodic initial value problems, J. Inst. Math. Appl. 18 (1976), no. 2, 189–202. MR 431691, DOI 10.1093/imamat/18.2.189
E. Stiefel and D. G. Bettis, Stabilization of Cowell’s method, Numer. Math. 13 (1969), 154–175. MR 263250, DOI 10.1007/BF02163234
R. M. Thomas, Phase properties of high order, almost $P$-stable formulae, BIT 24 (1984), no. 2, 225–238. MR 753550, DOI 10.1007/BF01937488

J. Comput. Phys.