An algebra of pseudo difference schemes and its applications

On the Stability of Finite Difference Schemes Which Approximate Regularly Hyperbolic Systems with Nearly Constant Coefficients

“…But for non-symmetric hyperbolic systems with variable coefficients there are much less results, except for few special examples (Friedrichs scheme, modified LaxWendroff scheme. (Yamaguti and Nogi [8]). …”

“…Here following the ideas of Yamaguti and Nogi [8] we introduce pseudo difference scheme to obtain local energy inequality for finite difference schemes which approximate nonsymmetric hyperbolic partial differential equations.…”

On the General Form of Yamaguti-Nogi-Vaillancourt's Stability Theorem

“…The theor} r of pseudo-difference and translation operators has played an important role in the stability theory of difference schemes as in [3], [14], [15], [17]. But the treatments of pseudo-difference operators are rather different from those of pseudo-differential operators, although it seems that both operators work in the same principle.…”

“…It is well known that the Friedrichs scheme is stable in many hyperbolic cases ( [2], [5], [10], [15], [17]) and it is quite natural that this simple scheme may be expected to be stable under less restriction.…”

“…14) , we can naturally derive a stability theorem of the Friedrichs scheme for a diagonalizable hyperbolic system by using the well known calculus of pseudo-differential operators. We should note that the theorem is regarded as the general form of the Yamaguti-Nogi-Vaillancourt stability theorm ( [14], [16], [17]) and holds without the restriction on the behavior of symbol p h (x y £) at x -oo.…”