Small-Stencil Pad Schemes to Solve Nonlinear Evolution Equations

LIU Ru-xun; WU Ling-ling

Volume 26 Issue 7

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 2005 > 26(7): 801-809

LIU Ru-xun, WU Ling-ling. Small-Stencil Pad Schemes to Solve Nonlinear Evolution Equations[J]. Applied Mathematics and Mechanics, 2005, 26(7): 801-809.

Citation:

LIU Ru-xun, WU Ling-ling. Small-Stencil Pad Schemes to Solve Nonlinear Evolution Equations[J]. Applied Mathematics and Mechanics, 2005, 26(7): 801-809.

Citation:

LIU Ru-xun, WU Ling-ling. Small-Stencil Pad Schemes to Solve Nonlinear Evolution Equations[J]. Applied Mathematics and Mechanics, 2005, 26(7): 801-809.

PDF( 357 KB)

Small-Stencil Pad Schemes to Solve Nonlinear Evolution Equations

Department of Mathematics, University of Science and Technology of China, Hefei 230026, P. R. China

Received Date: 2003-09-03
Rev Recd Date: 2005-03-11
Publish Date: 2005-07-15

Abstract

Abstract

A set of small-stencil new Pad schemes with the same denominator are presented to solve high-order non-linear evoltuion equations. Using this scheme, the fourth-order precision cannot only be kept, but also the final three-diagonal discrete systems are solved by simple Doolittle methods, or ODE systems by Runge-Kutta technique. Numerical samples show that the schemes are very satisfactory. And the advantage of the schemes is very clear compared to other finite difference schemes.
- evolution equation,
- compact scheme,
- Pad scheme,
- node stencil,
- soliton

FullText(HTML)

References(10)

References

[1]	Kahan W,LI Ren-chang.Unconventional schemes for a class of ordinary differential equations with applications to the Korteweg-de Vries equation[J].J Math Phys,1997,134(6)：316—331.
[2]	Gardner L R T,Gardner G A.Solitary waves of regularised long-wave equation[J].J Math Phys,1990,91:441—459.
[3]	Lele S K.Compact finite difference schemes with spectral-like resolution[J].Journal of Computational Physics,1992,103:16—42. doi: 10.1016/0021-9991(92)90324-R
[4]	Kobayashi M H.On a class of Pade finite volume methods[J].Journal of Computational Physics,1999,156(1):137—180. doi: 10.1006/jcph.1999.6376
[5]	Hixon R.Prefactored small-stencil compact schemes[J]. Journal of Computational Physics,2000,165(2):522—541. doi: 10.1006/jcph.2000.6631
[6]	Carpenter M H.Methodology and application to high-order compact schemes[J].Journal of Computational Physics,1994,111:220—236. doi: 10.1006/jcph.1994.1057
[7]	Goedheer W J,Potters J H H M.A compact finite scheme on a non-equidistant mesh[J].Journal of Computational Physics,1985,61:269—279. doi: 10.1016/0021-9991(85)90086-5
[8]	Ganosa J,Gazdag J.The Korteweq-de Vries-Burgers equation[J].Journal of Computational Physics,1977,23:293—403.
[9]	忻孝康，刘儒勋,蒋伯城.计算流体动力学[M].长沙：国防科技大学出版社,1989.
[10]	刘儒勋，舒其望.计算流体力学的某些新方法[M].北京：科学出版社,2003.

Relative Articles

[1]	WANG Yahui, GUO Cheng, DU Yulong. A 3rd-Order WENO Scheme for Stencil Smoothness Indicators Based on Mapping[J]. Applied Mathematics and Mechanics, 2025, 46(3): 394-411. doi: 10.21656/1000-0887.450150
[2]	GAO Jingying, HE Siriguleng, QING Mei, Eerdunbuhe. An Efficient Compact Difference Scheme for the Symmetric Regularized Long Wave Equation[J]. Applied Mathematics and Mechanics, 2025, 46(3): 412-424. doi: 10.21656/1000-0887.440374
[3]	QIU Tianwei, WEI Guangmei, SONG Yuxin, WANG Zhen. Novel Soliton Solutions to KdV-Type Equations Based on Physics-Informed Neural Networks[J]. Applied Mathematics and Mechanics, 2025, 46(1): 105-113. doi: 10.21656/1000-0887.450122
[4]	FENG Yihu1, 2. Solitary Travelling Wave Solutions to Strongly Nonlinear Wave Equations[J]. Applied Mathematics and Mechanics, 2019, 40(1): 89-96. doi: 10.21656/1000-0887.390054
[5]	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
[6]	FENG Yi-hu, SHI Lan-fang, WANG Wei-gang, MO Jia-qi. Travelling Wave Solution to a Class of Generalized Nonlinear Strong-Damp Disturbed Evolution Equations[J]. Applied Mathematics and Mechanics, 2015, 36(3): 315-324. doi: 10.3879/j.issn.1000-0887.2015.03.009
[7]	SHI Juan-rong, WU Qin-kuan, MO Jia-qi. Asymptotic Travelling Wave Soliton Solutions for Nonlinear Disturbed Generalized NNV Systems[J]. Applied Mathematics and Mechanics, 2015, 36(9): 1003-1010. doi: 10.3879/j.issn.1000-0887.2015.09.011
[8]	SHI Juan-rong, SHI Lan-fang, MO Jia-qi. Solutions to a Class of Nonlinear Strong-Damp Disturbed Evolution Equations[J]. Applied Mathematics and Mechanics, 2014, 35(9): 1046-1054. doi: 10.3879/j.issn.1000-0887.2014.09.010
[9]	ZOU Li, WANG Zhen, LIANG Hui, ZONG Zhi, ZOU Hao. Finding New Types of Peakon Solutions for FitzHugh-Nagumo Equation by an Analytical Technique[J]. Applied Mathematics and Mechanics, 2013, 34(11): 1141-1149. doi: 10.3879/j.issn.1000-0887.2013.11.003
[10]	ZOU Li, WANG Zhen, ZONG Zhi, ZOU Dong-yang, ZHANG Shuo. Solving shock wave with discontinuity by enhanced differential transform method (EDTM)[J]. Applied Mathematics and Mechanics, 2012, 33(12): 1465-1476. doi: 10.3879/j.issn.1000-0887.2012.12.008
[11]	Zainal Abdul Aziz, Dennis Ling Chuan Ching, Faisal Salah Yousif. Bifurcation of Rupturing Path by the Nonlinear Damping Force[J]. Applied Mathematics and Mechanics, 2011, 32(3): 271-278. doi: 10.3879/j.issn.1000-0887.2011.03.003
[12]	TU Guo-hua, YUAN Xiang-jiang, LU Li-peng. Developing Shock-Capturing Difference Methods[J]. Applied Mathematics and Mechanics, 2007, 28(4): 433-440.
[13]	TU Guo-hua, YUAN Xiang-jiang, XIA Zhi-qiang, HU Zhen. A Class of Compact Upwind TVD Difference Schemes[J]. Applied Mathematics and Mechanics, 2006, 27(6): 675-682.
[14]	LI Chun-jing, GU Chuan-qing. Epsilon-Algorithm and Eta-Algorithm of Generalized Inverse Function-Valued Padé Approximants Using for Solution of Integral Equations[J]. Applied Mathematics and Mechanics, 2003, 24(2): 197-204.
[15]	ZHANG Ren, SHA Wen-yu, JIANG Guo-rong, WANG Ji-guang. Soliton-Like Thermal Source Forcing and Singular Response of Atmosphere and Oceans to It[J]. Applied Mathematics and Mechanics, 2003, 24(6): 631-636.
[16]	TANG Deng-bin, XIA Hao. Nonlinear Evolution Analysis of T-S Disturbance Wave at Finite Amplitude in Nonparallel Boundary Layers[J]. Applied Mathematics and Mechanics, 2002, 23(6): 588-596.
[17]	TIAN Li-xin, XU Gang, LIU Zeng-rong. The Concave or Convex Peaked and Smooth Soliton Solutions of Camassa-Holm Equation[J]. Applied Mathematics and Mechanics, 2002, 23(5): 497-506.
[18]	GU Chuan-qing, LI Chun-jing. Computation Formulas of Generalised Inverse Padé Approximant Using for Solution of Integral Equations[J]. Applied Mathematics and Mechanics, 2001, 22(9): 952-958.
[19]	Xu Bao-zhi, Fang Xiao-wei. The Expression of Soliton Solution for Sine-Gordon Equation[J]. Applied Mathematics and Mechanics, 1992, 13(6): 515-518.
[20]	Yang Dan-ping. A Coupling Method of Difference with High Order Accuracy and Boundary Integral Equation for Evolutionary Equation and Its Error Estimates[J]. Applied Mathematics and Mechanics, 1991, 12(9): 831-844.