The Numerical Stabilities of Multiderivative Block Method

Kuang Jiao-xun; Lin Yu-hua

Volume 14 Issue 2

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1993 > 14(2): 119-126

Kuang Jiao-xun, Lin Yu-hua. The Numerical Stabilities of Multiderivative Block Method[J]. Applied Mathematics and Mechanics, 1993, 14(2): 119-126.

Citation:

Kuang Jiao-xun, Lin Yu-hua. The Numerical Stabilities of Multiderivative Block Method[J]. Applied Mathematics and Mechanics, 1993, 14(2): 119-126.

Citation:

Kuang Jiao-xun, Lin Yu-hua. The Numerical Stabilities of Multiderivative Block Method[J]. Applied Mathematics and Mechanics, 1993, 14(2): 119-126.

PDF( 442 KB)

The Numerical Stabilities of Multiderivative Block Method

Shanghai Normal University, Shanghai

Received Date: 1991-12-27
Publish Date: 1993-02-15

Abstract

Abstract

In [1],a class of multiderivative block methods(MDBM) was studied for the numerical solutions of stiff ordinary differential equations.This paper is aimed at solving the problem proposed in [1] that what conditions should be fulfilled for MDBMs in order to guarantee the A-stabilities.The explicit expressions of the polynomials P(h) and Q(h) in the stability functions ξ^k(h)=P(h)/Q(h)are given.Furthermore,we prove P(-h)=Q(h).With the aid of symbolic computations and the expressions of diagonal Fade approximations,we obtained the biggest block size k of the A-stable MDBM for any given l(the order of the highest derivatives used in MDBM,l≥1)
- multiderivative block methods,
- A-stability,
- block size

FullText(HTML)

References(3)

References

[1]	匡蛟勋,带有高阶导数的块隐式单步法,高校计算数学学报,9(1)(1987),15-23.
[2]	Watts,H.A.and L.E.Shampine:A-stable block implicit one-step methods,BIT,12(1972),252-266.
[3]	Birkhoff,G.and R.S.Varga,Discretization errors for well-set Cauchy problems(Ⅰ),J.Math,and Phys,4(1965),1-23.

Relative Articles

[1]	ZHU Dechun, ZHOU Jun, CAO Manxia, HUANG Wei. Block-Sparse Signal Recovery via l₂/l_q(q=2/3) Minimization[J]. Applied Mathematics and Mechanics, 2021, 42(9): 989-998. doi: 10.21656/1000-0887.420009
[2]	ZHANG Maolin, RAN Jing, ZHANG Shougui. A Self-Adaptive Uzawa Block Relaxation Method for Stokes Problems With Slip Boundary Conditions[J]. Applied Mathematics and Mechanics, 2021, 42(2): 188-198. doi: 10.21656/1000-0887.410170
[3]	WANG Zhen, DING Jieyu. A Multibody System Dynamics Vector Model and the Multistep Block Numerical Method[J]. Applied Mathematics and Mechanics, 2020, 41(12): 1323-1335. doi: 10.21656/1000-0887.400340
[4]	LI Bowen, DING Jieyu, LI Yanan. An L-Stable Method for Differential-Algebraic Equations of Multibody System Dynamics[J]. Applied Mathematics and Mechanics, 2019, 40(7): 768-779. doi: 10.21656/1000-0887.400038
[5]	GUO Nanxin, ZHANG Shougui. A Self-Adaptive Uzawa Block Relaxation Algorithm for Free Boundary Problems[J]. Applied Mathematics and Mechanics, 2019, 40(6): 682-693. doi: 10.21656/1000-0887.390347
[6]	ZHOU Jun, HUANG Wei. Improved Conditions for Block-Sparse Signal Recovery via the Non-Convex Optimization Model[J]. Applied Mathematics and Mechanics, 2019, 40(2): 167-180. doi: 10.21656/1000-0887.390154
[7]	CHEN Peng-qing, HUANG Wei. Block-Sparse Signal Recovery Based on l₁-l₂Norm Minimization[J]. Applied Mathematics and Mechanics, 2017, 38(8): 932-942. doi: 10.21656/1000-0887.370230
[8]	J.C.Misra, S.Maiti. Peristaltic Transport of a Rheological Fluid: Model for Movement of Food Bolus Through Esophagus[J]. Applied Mathematics and Mechanics, 2012, 33(3): 303-319. doi: 10.3879/j.issn.1000-0887.2012.03.004
[9]	DING Liang, HAN Bo, LIU Jia-qi. Wavelet Multiscale Method for the Inversion of Maxwell’s Equation[J]. Applied Mathematics and Mechanics, 2009, 30(8): 970-978. doi: 10.3879/j.issn.1000-0887.2009.08.010
[10]	HU Wei-peng, DENG Zi-chen. Multi-Symplectic Method for Generalized Boussinesq Equation[J]. Applied Mathematics and Mechanics, 2008, 29(7): 839-845.
[11]	LIU Jian-zhou, HUANG Ze-jun. Note on “Block H-Matrices and Spectrum of Block Matrices”[J]. Applied Mathematics and Mechanics, 2008, 29(7): 864-870.
[12]	HU Wei-peng, DENG Zi-chen, LI Wen-cheng. Multi-Symplectic Methods for Membrane Free Vibration Equation[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1054-1062.
[13]	HAN Zhi-jun, CHENG Guo-qiang, MA Hong-wei, ZHANG Shan-yuan. Dynamic Buckling of Elastic-Plastic Column Impacted by a Rigid Body[J]. Applied Mathematics and Mechanics, 2006, 27(3): 337-341.
[14]	SHAO Xue-ming, LIU Yang, YU Zhao-sheng. Interactions Between Two Sedimenting Particles With Different Sizes[J]. Applied Mathematics and Mechanics, 2005, 26(3): 372-378.
[15]	CAI Zi-li, QU Wei-dong, XI Yu-geng. Dynamic Modeling for Airship Equipped With Ballonets and Ballast[J]. Applied Mathematics and Mechanics, 2005, 26(8): 979-987.
[16]	GU Tong-xiang, CHI Xue-bin, LIU Xing-ping. AINV and BILUM Preconditioning Techniques[J]. Applied Mathematics and Mechanics, 2004, 25(9): 927-934.
[17]	HUANG Ting-zhu, LI Wen. Block H-Matrices and Spectrum of Block Matrices[J]. Applied Mathematics and Mechanics, 2002, 23(2): 217-220.
[18]	Zhao Weijia, Pan Zhenkuan, Wang Yibing. An Automatic Constraint Violation Stabilization Method for Differential/Algebraic Equations of Motion Multibody System Dynamics[J]. Applied Mathematics and Mechanics, 2000, (1): 94-98.
[19]	Deng Chang-gen. The Activation Method for Discretized Conservative Nonlinear Stability Problems with Multiple Parameter and State Variables[J]. Applied Mathematics and Mechanics, 1993, 14(10): 873-881.
[20]	Tsai Shu-tang, Ma Bai-kun. A New Turbulence Model with the Separate Consideration of Large and Small Vortexes[J]. Applied Mathematics and Mechanics, 1987, 8(10): 849-858.