Numerical approximation of fractional powers of regularly accretive operators

Numerical Approximation of Fractional Powers of Regularly Accretive Operators

We study the numerical approximation of fractional powers of accretive operators in this paper. Namely, if A is the accretive operator associated with an accretive sesquilinear form A(·, ·) defined on a Hilbert space V contained in L(Ω), we approximate A for β ∈ (0, 1). The fractional powers are defined in terms of the so-called Balakrishnan integral formula. Given a finite element approximatio...

Numerical approximation of fractional powers of elliptic operators

We present and study a novel numerical algorithm to approximate the action of T := L where L is a symmetric and positive definite unbounded operator on a Hilbert space H0. The numerical method is based on a representation formula for T in terms of Bochner integrals involving (I + tL) for t ∈ (0,∞). To develop an approximation to T , we introduce a finite element approximation Lh to L and base o...

On the Sum of Fractional Derivatives and M-accretive Operators

The approximation of parabolic equations involving fractional powers of elliptic operators

We study the numerical approximation of a time dependent equation involving fractional powers of an elliptic operator L defined to be the unbounded operator associated with a Hermitian, coercive and bounded sesquilinear form on H 0 (Ω). The time dependent solution u(x, t) is represented as a Dunford Taylor integral along a contour in the complex plane. The contour integrals are approximated usi...

Domination number of graph fractional powers

For any $k in mathbb{N}$, the $k$-subdivision of graph $G$ is a simple graph $G^{frac{1}{k}}$, which is constructed by replacing each edge of $G$ with a path of length $k$. In [Moharram N. Iradmusa, On colorings of graph fractional powers, Discrete Math., (310) 2010, No. 10-11, 1551-1556] the $m$th power of the $n$-subdivision of $G$ has been introduced as a fractional power of $G$, denoted by ...