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Ding, Heng-Fei; Zhang, Yu-Xin; Cao, Jian-Xiong; Tian, Jun-Hong

A class of difference scheme for solving telegraph equation by new non-polynomial spline methods. (English) Zbl 1244.65124

Appl. Math. Comput. 218, No. 9, 4671-4683 (2012).
Summary: By using a new non-polynomial parameters cubic splines in space direction and compact finite differences 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 the solving telegraph equation if we suitably choose the cubic spline parameters. Meanwhile, stability condition of the difference scheme are carried out. Finally, numerical examples are used to illustrate the efficiency of the new difference scheme.

Cited in 16 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Keywords:

telegraph equation; non-polynomial spline; finite difference scheme; high accuracy; truncation error; stability; numerical examples
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\textit{H.-F. Ding} et al., Appl. Math. Comput. 218, No. 9, 4671--4683 (2012; Zbl 1244.65124)
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