Results 141 to 150 of about 53,909 (198)
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Optimal finite-difference schemes for elastic wave based on improved cosine-combined window function
, 2020The finite difference method is widely used in seismic wave numerical simulation, reverse time migration and full waveform inversion. However, the numerical dispersion problem seriously affects the results of seismic imaging and inversion. Based on this,
Ling Wen-da +6 more
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On Maximal Regularity and Semivariation of Cosine Operator Functions
Journal of the London Mathematical Society, 1999Summary: It is proved that a cosine operator function \(C(\cdot)\), with generator \(A\), is locally of bounded semivariation if and only if \(u''(t)= Au(t)+ f(t)\), \(t> 0\), \(u(0)\), \(u'(0)\in D(A)\), has a strong solution for every continuous function \(f\), if and only if the function \[ \int^t_0 \int^{t-s}_0 C(\tau) f(s) d\tau ds, \] \(t>0\), is
Chyan, D.-K., Shaw, S.-Y., Piskarev, S.
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Discrete Approximations of Cosine Operator Functions. I
SIAM Journal on Numerical Analysis, 1982Summary: We are concerned with the approximation of cosine operator functions which appear in a natural way in the study of the Cauchy problem for second order evolution equations. We derive both qualitative and quantitative convergence theorems characterizing the convergence of cosine operator functions in terms of their infinitesimal generators, and ...
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Semigroups of operators, cosine operator functions, and linear differential equations
Journal of Soviet Mathematics, 1991This survey presents a systematic review of the theory of strongly continuous semigroups and cosine functions on Banach spaces as developed from the early beginning up to 1989. It contains the following nine sections: 1. Linear differential equations in Banach spaces 2. Semigroups of operators of the class \(C_ 0\) 3. Cosine and sine operator functions
Vasil'ev, V. V. +2 more
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Approximation of cosine functions and Rogosinski type operators [PDF]
, 2011 We study some quantitative estimates of the convergence of the iterates of some Rogosinski type operators to their associated cosine functions. We also consider a general cosine counterpart of the quantitative version of Trotter’s theorem on the approximation of C0-semigroups.
CAMPITI, Michele +2 more
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Integrated C -Semigroups and C -Cosine Functions of Hermitian and Positive Operators
, 2000Some recent results on n-times integrated C-semigroups and C-cosine functions of hermitian and positive operators on Banach spaces are discussed. The following are some interesting properties: 1) A hermitian n-times integrated C-semigroup T() (resp. C-cosine function C()) is (n — 1)-th continuously differentiable in operator norm on [0, ∞) and T( n-1 )
Yuan-Chuan Li, S. Shaw
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About a complex operator exponential function of a complex operator argument main property
Tambov University Reports. Series: Natural and Technical Sciences, 2019Operator functions e^A, sin B, cos B of the operator argument from the Banach algebra of bounded linear operators acting from E to E are considered in the Banach space E .
V. Fomin
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AIP Conference Proceedings, 2011
Cauchy problem for a quasi‐linear abstract hyperbolic equation is considered, where the main operator is self‐adjoint positive definite and represents a finite sum of its similar operators. For this problem the fourth order accuracy three‐layer decomposition scheme is constructed on the basis of rational splitting of the cosine operator‐function.
J. Rogava, M. Tsiklauri
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Cauchy problem for a quasi‐linear abstract hyperbolic equation is considered, where the main operator is self‐adjoint positive definite and represents a finite sum of its similar operators. For this problem the fourth order accuracy three‐layer decomposition scheme is constructed on the basis of rational splitting of the cosine operator‐function.
J. Rogava, M. Tsiklauri
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On the spectrum of cosine operator functions
Integral Equations and Operator Theory, 1989Let C(t), \(t\in {\mathbb{R}}\), be a strongly continuous cosine function, defined in a Hilbert space H, with infinitesimal generator A. Let \(\rho\) (A) and \(\sigma\) (A) denote the resolvent set and the spectrum of A respectively. It is known that for certain classes of cosine functions, including the class of uniformly bounded cosine functions, the
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Norm Inequalities for Generators of Analytic Semigroups and Cosine Operator Functions
Canadian Mathematical Bulletin, 1989AbstractWe prove that if A is the infinitesimal generator of a bounded analytic semigroup in a sector {z ∊ C : |arg z| ≦ (απ)/2} of bounded linear operators on a Banach space, then the following inequalities hold:for any x ∊ D(An) and for any 0 < β < α. This result helps us to answer in affirmative a question raised by M. W. Certain and T.
Siddiqi, Jamil A., Elkoutri, Abdelkader
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