An unconditionally stable spline difference scheme of O(k2+h4) for solving the second-order 1D linear hyperbolic equation

In this paper, the second-order linear hyperbolic equation is solved by using a new three-level difference scheme based on quartic spline interpolation in space direction and finite difference discretization in time direction. Stability analysis of the scheme is carried out. The proposed scheme is second-order accurate in time direction and fourth-order accurate in space direction. Finally, numerical examples are tested and results are compared with other published numerical solutions.

[1]  R. K. Mohanty New unconditionally stable difference schemes for the solution of multi-dimensional telegraphic equations , 2009, Int. J. Comput. Math..

[2]  R. K. Mohanty,et al.  On the use of high order difference methods for the system of one space second order nonlinear hyperbolic equations with variable coefficients , 1996 .

[3]  M. Ciment,et al.  A note on the operator compact implicit method for the wave equation , 1978 .

[4]  R. K. Mohanty,et al.  An unconditionally stable alternating direction implicit scheme for the two space dimensional linear hyperbolic equation , 2001 .

[5]  John J. H. Miller On the Location of Zeros of Certain Classes of Polynomials with Applications to Numerical Analysis , 1971 .

[6]  E. H. Twizell An explicit difference method for the wave equation with extended stability range , 1979 .

[7]  Feng Gao,et al.  Unconditionally stable difference schemes for a one-space-dimensional linear hyperbolic equation , 2007, Appl. Math. Comput..

[8]  R. K. Mohanty,et al.  An Unconditionally Stable ADI Method for the Linear Hyperbolic Equation in Three Space Dimensions , 2002, Int. J. Comput. Math..

[9]  S. Sallam,et al.  A quartic C 3 -spline collocation method for solving second-order initial value problems , 1996 .

[10]  R. K. Mohanty An unconditionally stable difference scheme for the one-space-dimensional linear hyperbolic equation , 2004, Appl. Math. Lett..

[11]  R. K. Mohanty,et al.  A new discretization method of order four for the numerical solution of one-space dimensional second-order quasi-linear hyperbolic equation , 2002 .