A class of difference scheme for solving telegraph equation by new non-polynomial spline methods

被引：25

作者：

Ding, Heng-fei ^{[1
,2
]}

Zhang, Yu-xin ^{[2
]}

Cao, Jian-xiong ^{[1
]}

Tian, Jun-hong ^{[2
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

[2] Tianshui Normal Univ, Sch Math & Stat, Tianshui 741001, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2012年 / 218卷 / 09期

关键词：

Telegraph equation; Non-polynomial spline; Finite difference scheme; High accuracy; Truncation error; Stability analysis; LINEAR HYPERBOLIC EQUATION; VARIABLE-COEFFICIENTS; APPROXIMATION;

D O I：

10.1016/j.amc.2011.10.078

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, by using a new non-polynomial parameters cubic spline in space direction and compact finite difference in time direction, we get a class of new high accuracy scheme of O(tau(4) + h(2)) and O(tau(4) + h(4)) for solving telegraph equation if we suitably choose the cubic spline parameters. Meanwhile, stability condition of the difference scheme has been carried out. Finally, numerical examples are used to illustrate the efficiency of the new difference scheme. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：4671 / 4683

页数：13

共 16 条

[1] A spline method for second-order singularly perturbed boundary-value problems [J].

Aziz, T ;

Khan, A .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2002, 147 (02) :445-452

[2] An Approximation to the Solution of Telegraph Equation by Variational Iteration Method [J].

Biazar, J. ;

Ebrahimi, H. ;

Ayati, Z. .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2009, 25 (04) :797-801

[3]

Biazar J., 2007, International Mathematical Forum, V2 of 45, P2231, DOI DOI 10.12988/IMF.2007.07196

[4] A new fourth-order compact finite difference scheme for the two-dimensional second-order hyperbolic equation [J].

Ding, Hengfei ;

Zhang, Yuxin .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 230 (02) :626-632

[5] A new unconditionally stable compact difference scheme of O(τ2 + h4) for the 1D linear hyperbolic equation [J].

Ding, Hengfei ;

Zhang, Yuxin .

APPLIED MATHEMATICS AND COMPUTATION, 2009, 207 (01) :236-241

[6] Unconditionally stable difference schemes for a one-space-dimensional linear hyperbolic equation [J].

Gao, Feng ;

Chi, Chunmei .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 187 (02) :1272-1276

[7]

Jain M.K., 1984, NUMERICAL SOLUTION D

[8] A survey on parametric spline function approximation [J].

Khan, A ;

Khan, I ;

Aziz, T .

APPLIED MATHEMATICS AND COMPUTATION, 2005, 171 (02) :983-1003

[9] An unconditionally stable finite difference formula for a linear second order one space dimensional hyperbolic equation with variable coefficients [J].

Mohanty, RK .

APPLIED MATHEMATICS AND COMPUTATION, 2005, 165 (01) :229-236

[10] On the use of high order difference methods for the system of one space second order nonlinear hyperbolic equations with variable coefficients [J].

Mohanty, RK ;

Jain, MK ;

George, K .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1996, 72 (02) :421-431

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