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

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- 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
L. Brusa & L. Nigro, "A one-step method for direct integration of structural dynamic equations," - 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
R. van Dooren, "Stabilization of Cowell’s classical finite difference method for numerical integration,"

*Internat. J. Numer. Methods Engrg.*, v. 15, 1980, pp. 685-699.

*J. Comput. Phys.*, v. 16, 1974, pp. 186-192.

## Additional Information

- © Copyright 1987 American Mathematical Society
- Journal: Math. Comp.
**49**(1987), 553-559 - MSC: Primary 65L05
- DOI: https://doi.org/10.1090/S0025-5718-1987-0906188-X
- MathSciNet review: 906188