Stability Theory for Difference Approximations
ثبت نشده
چکیده
are given, u1 and u11 are defined according to the partition of A, i.e. u1 = (wU), • • -, um)', ulL = (w<!+1), • • -, uM)', and *S is a given constant rectangular matrix. It is well known that the above problem is correctly posed in L2 (see for example Thomée [4]). The present treatment of the case when A is a constant matrix can be extended, as in [1], to the case when A depends on (x, t) in a sufficiently smooth fashion. In the earlier paper [1], we considered the case when the coefficient matrices of the difference schemes were diagonal. The same class of problems has also been treated in an interesting paper by Osher [2]. The assumption of diagonality would
منابع مشابه
Stability Theory of Difference Approximations for Multidimensional Initial-Boundary Value Problems
A stability theory is developed for dissipative difference approximations to multidimensional initial-boundary value problems. The original differential problem should be strictly hyperbolic and the difference problem consistent with the differential one. An algebra of pseudo-difference operators is built and later used to prove the stability of the difference approximation with variable coeffi...
متن کاملL1-Stability and error estimates for approximate Hamilton-Jacobi solutions
We study theL1-stability and error estimates of general approximate solutions for the Cauchy problem associated with multidimensional Hamilton-Jacobi (H-J) equations. For strictly convex Hamiltonians, we obtain a priori error estimates in terms of the truncation errors and the initial perturbation errors. We then demonstrate this general theory for two types of approximations: approximate solut...
متن کاملStability and Convergence of Difference Approximations to Pseudo-Parabolic Partial Differential Equations
Two difference approximations to the solution of a pseudo-parabolic problem are constructed and shown by means of stability analysis to converge in the "discrete" £2 norm. A relation between parabolic and pseudo-parabolic difference schemes is discussed, and the stability of difference approximations to backward time parabolic and pseudo-parabolic problems is also considered.
متن کاملThe Semigroup Stability of the Difference Approximations for Initial-boundary Value Problems
For semidiscrete approximations and one-step fully discretized approximations of the initial-boundary value problem for linear hyperbolic equations with diagonalizable coefficient matrices, we prove that the Kreiss condition is a sufficient condition for the semigroup stability (or l2 stability). Also, we show that the stability of a fully discretized approximation generated by a locally stable...
متن کاملAb-initio study of Electronic, Optical, Dynamic and Thermoelectric properties of CuSbX2 (X=S,Se) compounds
Abstract: In this work we investigate the electronic, optical, dynamic and thermoelectric properties of ternary copper-based Chalcogenides CuSbX2 (X= S, Se) compounds. Calculations are based on density functional theory and the semi-classical Boltzmann theory. Computations have been carried out by using Quantum-Espresso (PWSCF) package and ab-initio pseudo-potential technique. To estimate the e...
متن کاملCommon Fixed Points and Invariant Approximations for Cq-commuting Generalized nonexpansive mappings
Some common fixed point theorems for Cq-commuting generalized nonexpansive mappings have been proved in metric spaces. As applications, invariant approximation results are also obtained. The results proved in the paper extend and generalize several known results including those of M. Abbas and J.K. Kim [Bull. Korean Math. Soc. 44(2007) 537-545], I. Beg, N. Shahzad and M. Iqbal [Approx. Theory A...
متن کامل