An operator splitting technique for an unconditionally stable difference method for a linear three space dimensional hyperbolic equation with variable coefficients

We report a new three-step operator splitting method of O( k 2+ h 2) for the difference solution of linear hyperbolic equation u tt +2 α( x, y, z, t) u t + β 2( x, y, z, t) u= A( x, y, z, t) u xx + B( x, y, z, t) u yy + C( x, y, z, t) u zz + f( x, y, z, t) subject to appropriate initial and Dirichle...

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Bibliographic Details
Published in:Applied mathematics and computation 2005-03, Vol.162 (2), p.549-557
Main Author: Mohanty, R.K.
Format: Article
Language:English
Subjects:
Difference and functional equations, recurrence relations
Exact sciences and technology
Finite differences and functional equations
Functional analysis
Implicit scheme
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Operator splitting method
Partial differential equations
RMS errors
Sciences and techniques of general use
Singular equation
Telegraph equation
Unconditionally stable
Variable coefficients
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Summary:We report a new three-step operator splitting method of O( k 2+ h 2) for the difference solution of linear hyperbolic equation u tt +2 α( x, y, z, t) u t + β 2( x, y, z, t) u= A( x, y, z, t) u xx + B( x, y, z, t) u yy + C( x, y, z, t) u zz + f( x, y, z, t) subject to appropriate initial and Dirichlet boundary conditions, where α( x, y, z, t)> β( x, y, z, t)>0 and A( x, y, z, t)>0, B( x, y, z, t)>0, C( x, y, z, t)>0. The method is applicable to singular problems and stable for all choices of h>0 and k>0. The resulting system of algebraic equations is solved by using a tri-diagonal solver. Computational results are provided to demonstrate the viability of the new method.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2003.12.135