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The cubic-interpolated pseudo particle (CIP) method: Application to nonlinear and multi-dimensional hyperbolic equations. (English) Zbl 0624.65079
A generalization of the CIP method, proposed previously by the authors for solving linear one-dimensional hyperbolic equations, to multi- dimensional and nonlinear problems is developed. The method gives stable and less diffusive results for square wave propagation compared with various schemes.
Reviewer: V.A.Kostova

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L60 First-order nonlinear hyperbolic equations
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[1] Takewaki, H.; Nishiguchi, A.; Yabe, T., J. comput. phys., 61, 261, (1985)
[2] Shouri, M.M., J. comput. phys., 49, 334, (1983)
[3] Knorr, G.; Mond, M., J. comput. phys., 38, 212, (1980)
[4] Boris, J.P.; Book, D.L., J. comput. phys., 11, 38, (1973)
[5] Lax, P.D.; Wendroff, B., Comm. pure appl. math., 13, 217, (1960)
[6] Lax, P.D., Comm. pure appl. math., 11, 175, (1958)
[7] Fromm, J.E., J. comput. phys., 3, 176, (1968)
[8] Hirsh, R.S., J. comput. phys., 19, 90, (1975)
[9] Book, D.L.; Boris, J.P.; Hain, K., J. comput. phys., 18, 248, (1975)
[10] Nishiguchi, A.; Yabe, T., J. comput. phys., 52, 390, (1983)
[11] Evans, M.W.; Harlow, F.H.; Harlow, F.H.; Amsden, A.A., The particle-in-cell method for the calculation of the dynamic of compressive fluids, (), Los alamos scientific laboratory report LA-3466, (1966), Los Alamos, NM
[12] Wilkins, M.L., J. comput. phys., 36, 281, (1980)
[13] Harten, A.; Zwas, G., J. comput. phys., 9, 568, (1972)
[14] McRae, G.J.; Goodin, W.R.; Seinfeld, J.H., J. comput. phys., 45, 1, (1982)
[15] MacCormack, R.W., AIAA paper, 69-354, (1969)
[16] Zalesak, S.T., J. comput. phys., 31, 335, (1979)
[17] Sod, G.A., J. comput. phys., 27, 1, (1978)
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