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High order finite difference schemes with application to wave propagation problems. (English) Zbl 1165.65383

From the abstract: We consider the approximate solution to wave propagation problems by a family of fully discrete finite difference implicit schemes. The stability of mixed initial boundary problems is investigated. A wide series of computational experiments is performed.

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76M20 Finite difference methods applied to problems in fluid mechanics
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References:

[1] M.A. Pirozzi , High-accuracy finite difference methods for systems of conservation laws. I , Technical Report, Istituto di Matematica , Istituto Universitario Navale , Marzo 1999 .
[2] M.A. Pirozzi , A class of semi-implicit schemes for wave propagation problems , Annali dell’Istituto Universitario Navale , vol. LXIII ( 1997 ), pp. 7 - 10 .
[3] M.A. Pirozzi , Numerical simulation of fluid dynamic problems on distributed memory parallel computers , Concurrency: Practice and Experience, vol. 9 ( 1997 ), pp. 989 - 998 . Zbl 0895.76059 · Zbl 0895.76059
[4] M.A. Pirozzi , On boundary conditions for the numerical solution of fluid dynamic problems , Calcolo , 26 ( 10 ) ( 1989 ), pp. 149 - 165 . MR 1083051 | Zbl 0708.76045 · Zbl 0708.76045 · doi:10.1007/BF02575726
[5] M.A. Pirozzi , Sulla stabilità di condizioni all’interfaccia nel raffinamento dei reticoli , Atti del Convegno Nazionale di Analisi Numerica , 1989 , pp. 413 - 422 .
[6] A. Lerat - Z. N. WU, Stable conservative multidomain treatments for implicit Euler solvers , J. Comput. Phys. , 123 ( 1996 ), pp. 45 - 64 . MR 1370375 | Zbl 0839.76065 · Zbl 0839.76065 · doi:10.1006/jcph.1996.0004
[7] C.A.J. Fletcher , Computational techniques for fluid dynamics 1 , Springer Verlag , 1991 . MR 1104657 | Zbl 0717.76001 · Zbl 0717.76001
[8] G.A. Sod , Numerical methods in fluid dynamics , Cambridge University Press , 1989 . MR 832441 | Zbl 0592.76001 · Zbl 0592.76001 · doi:10.1017/CBO9780511753138
[9] R.D. Richtmyer - K. W. MORTON, Difference methods for initial-value problems, 2nd eds ., J. Wiley , 1967 . MR 220455 | Zbl 0155.47502 · Zbl 0155.47502
[10] D.R. Emerson et al., Parallel computational fluid dynamics , Elsevier Science B. V. , 1998 . MR 1634267 · Zbl 0895.68148
[11] A. Quarteroni - A. Valli , Numerical approximation of partial differential equations , Springer Verlag , 1994 . MR 1299729 | Zbl 0803.65088 · Zbl 0803.65088
[12] C.A.J. Fletcher , Computational techniques for fluid dynamics 2 , Springer Verlag , 1991 . MR 1122807 | Zbl 0717.76001 · Zbl 0717.76001
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