×

On the use of high order difference methods for the system of one space second order nonlinear hyperbolic equations with variable coefficients. (English) Zbl 0877.65066

Three level-implicit difference schemes of order 4 are developed for initial-boundary value problems for a linear system of wave equations with variable coefficients and nonlinear lower-order terms. The difference scheme is particularly adapted for the singular lower-order term arising at the origin when solving the scalar wave equations in cylindrical and spherical symmetry. A linear stability analysis is performed. The convergence order is verified on numerical examples.

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
35L70 Second-order nonlinear hyperbolic equations
35L05 Wave equation
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ciment, M.; Leventhal, S. H., Higher order compact implicit schemes for the wave equation, Math. Comp., 29, 985-994 (1975) · Zbl 0309.35043
[2] Ciment, M.; Leventhal, S. H., A note on the operator compact implicit method for the wave equation, Math. Comp., 32, 143-147 (1978) · Zbl 0373.35039
[3] Greenspan, D., Approximate solution of initial boundary wave equation problems by boundary value techniques, Comm. ACM, 11, 760-763 (1968) · Zbl 0176.15304
[4] Jain, M. K.; Jain, R. K.; Mohanty, R. K., Fourth order difference methods for the system of 2-D nonlinear elliptic partial differential equations, Numer. Methods Partial Differential Equations, 7, 227-244 (1991) · Zbl 0735.65072
[5] Jain, M. K.; Jain, R. K.; Mohanty, R. K., The numerical solution of the two-dimensional unsteady Navier-Stokes equations using fourth order difference method, Internat. J. Comput. Math., 39, 125-134 (1991) · Zbl 0744.76084
[6] Jain, M. K.; Jain, R. K.; Mohanty, R. K., High order difference methods for the system of one-dimensional second order hyperbolic equations with nonlinear first derivative terms, J. Mat. Phy. Sci., 26, 401-411 (1992) · Zbl 0778.65060
[7] Mohanty, R. K., Fourth order finite difference methods for the system of 2-D nonlinear elliptic equations with variable coefficients, Internat. J. Comput. Math., 46, 195-206 (1992) · Zbl 0816.76060
[8] Roisin, B. C., Analytical linear stability criteria for the leap-frog, Dufort-Frankel method, J. Comput. Phys., 53, 227-239 (1984) · Zbl 0571.76091
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.