Strong stability preserving (SSP) high order time discretizations were developed to ensure nonlinear stability properties necessary in the numerical solution of hyperbolic partial differential equations with discontinuous solutions. SSP methods preserve the strong stability properties – in any norm, seminorm or convex functional – of the spatial discretization coupled with first order Euler tim...

The fractal image coding technique has attracted a degree of interest for its low bit rate. But the reconstructed image is of medium quality. This problem has prevented the fractal technique from being practically used. In order to improve the compression fidelity, a new affine transformation is proposed in this paper. Meanwhile, its contractivity requirement is analyzed, and the optimal parame...

Let M be a compact Riemannian manifold without boundary. Consider the porous media equation u̇ = 4(um), u(0) = u0 ∈ Lq , 4 being the Laplace–Beltrami operator. Then, if q ≥ 2 ∨ (m − 1), the associated evolution is Lq − L∞ regularizing at any time t > 0 and the bound ‖u(t)‖∞ ≤ C(u0)/t (1) holds for t < 1 for suitable explicit C(u0), γ. For large t it is shown that, for general initial data, u(t) ...

In this paper, we investigate the longtime behavior of time fractional reaction–diffusion equations with delay. The governing partial differential equation generalizes Hutchinson, Mackey–Glass and Nicholson’s blowflies equations. Energy estimates, asymptotic stability contractivity problem are proved. finite difference technique is used to discretize time-fractional Caputo derivative, spectral ...

We analyze the one dimensional Cucker–Smale (in short CS) model with a weak singular communication weight ψ(x)=|x|−β β∈(0,1). first establish global-in-time existence of measure-valued solutions to kinetic CS equation. For this, we use proper change variable reformulate particle as first-order system and provide uniform-in-time stability for that system. then extend this estimate By using estim...

In this paper, we introduce the new concept of mutual Reich contraction that involves a pair operators acting on distance space. We chose framework strong b-metric spaces (generalizing standard metric spaces) in order to add more extended underlying structure. provide sufficient conditions for two mutually contractive maps have common fixed point. The result is family any cardinality. dynamics ...

The sum-product or belief propagation (BP) algorithm is a widely used message-passing technique for computing approximate marginals in graphical models. We introduce a new technique, called stochastic orthogonal series message-passing (SOSMP), for computing the BP fixed point in models with continuous random variables. It is based on a deterministic approximation of the messages via orthogonal ...