Related papers: Oscillation-free method for semilinear diffusion e…
Interactions of supersonic uniform streams with cylindrical bodies, placed in open channels, are studied. Channels of rotation with the interval of cross-sectional area decreasing are considered. Two-dimensional Euler equations are solved…
In this paper, a higher-order time-discretization scheme is proposed, where the iterates approximate the solution of the stochastic semilinear wave equation driven by multiplicative noise with general drift and diffusion. We employ a…
We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…
A well-known issue associated with the use of fully conservative schemes in multicomponent-flow simulations is the generation of spurious pressure oscillations at contact interfaces. These oscillations can rapidly lead to solver divergence…
The error behavior of exponential operator splitting methods for nonlinear Schr{\"o}dinger equations in the semiclassical regime is studied. For the Lie and Strang splitting methods, the exact form of the local error is determined and the…
We propose a new class of semi-implicit methods for solving nonlinear fractional differential equations and study their stability. Several versions of our new schemes are proved to be unconditionally stable by choosing suitable parameters.…
A practical and simple stable method for calculating Fourier integrals is proposed, effective both at low and at high frequencies. An approach based on the fruitful idea of Levin, to use of the collocation method to approximate the slowly…
Amplification is usually necessary when measuring the frequency instability of microwave signals. In this work, we develop a flicker noise free frequency measurement system based on a common or shared amplifier. First, we show that…
We deal with a class of semilinear nonlocal differential equations in Hilbert spaces which is a general model for some anomalous diffusion equations. By using the theory of integral equations with completely positive kernel together with…
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…
Using spatial domain techniques developed by the authors and Myunghyun Oh in the context of parabolic conservation laws, we establish under a natural set of spectral stability conditions nonlinear asymptotic stability with decay at Gaussian…
We generalize our earlier results concerning meshfree collocation methods for semilinear elliptic second order problems to the quasilinear case. The stability question, however, is treated differently, namely by extending a paper on…
We present two novel additions to the semi-analytic solution of Lyman $\alpha$ (Ly$\alpha$) radiative transfer in spherical geometry: (1) implementation of the correct boundary condition for a steady source, and (2) solution of the…
We study the Cauchy problem for Schr\"odinger type stochastic partial differential equations with uniformly bounded coefficients on a curved space. We give conditions on the coefficients, on the drift and diffusion terms, on the Cauchy…
In the last three decades, powerful computer-assisted techniques have been developed in order to validate a posteriori numerical solutions of semilinear elliptic problems of the form $\Delta u +f(u,\nabla u) = 0$. By studying a well chosen…
This paper presents a new strategy to deal with the excessive diffusion that standard finite volume methods for compressible Euler equations display in the limit of low Mach number. The strategy can be understood as using centered…
We construct oscillatory solutions of fully semilinear wave equations in Minkowski space satisfying a null condition of the form $$\square u:=(-\partial_{x_0}^2 +\sum_{j=1}^n \partial_{x_j}^2 )u=…
We prove a modification to the classical maximal inequality for stochastic convolutions in 2-smooth Banach spaces using the factorization method. This permits to study semilinear stochastic partial differential equations with unbounded…
A short gas discharge layer sandwiched with a semiconductor layer between planar electrodes shows a variety of spatio-temporal patterns. The paper focusses on the spatially homogeneous spontaneous oscillations while a DC voltage is applied;…
We consider a non-linear variant of the transport-diffusion osmosis model for solving a variety of imaging problems such as shadow/soft-light removal and compact data representation. The non-linear behaviour is encoded in terms of a general…