相关论文: A short-memory operator splitting scheme for const…

In recent years, SPDEs have become a well-studied field in mathematics. With their increase in popularity, it becomes important to efficiently approximate their solutions. Thus, our goal is a contribution towards the development of…

Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…

Identifying differential operators from data is essential for the mathematical modeling of complex physical and biological systems where massive datasets are available. These operators must be stable for accurate predictions for dynamics…

This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…

Given that quantum error correction processes are unreliable, an efficient error syndrome extraction circuit should use fewer ancillary qubits, quantum gates, and measurements, while maintaining low circuit depth, to minimizing the circuit…

In this paper, we develop a physics-informed deep operator learning framework for solving multi-term time-fractional mixed diffusion-wave equations (TFMDWEs). We begin by deriving an $L_2$ approximation, which achieves first-order accuracy…

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the $H^{-1}$-gradient flow of the…

In this paper, we consider the numerical approximation of time-fractional parabolic problems involving Caputo derivatives in time of order $\alpha$, $0< \alpha<1$. We derive optimal error estimates for semidiscrete Galerkin FE type…

Quantum data encoding (QDE) enables faster com-putations than classical algorithms through superposition and en-tanglement. Circuit cutting and knitting are effective techniques for ameliorating current noisy quantum processing unit (QPUs)…

We present a new tunably-accurate Laguerre Petrov-Galerkin spectral method for solving linear multi-term fractional initial value problems with derivative orders at most one and constant coefficients on the half line. Our method results in…

The multi-term time-fractional mixed diffusion-wave equations (TFMDWEs) are considered and the numerical method with its error analysis is presented in this paper. First, a $L2$ approximation is proved with first order accuracy to the…

Damped wave equations have been used in many real-world fields. In this paper, we study a low-rank solution of the strongly damped wave equation with the damping term, visco-elastic damping term and mass term. Firstly, a second-order finite…

Supported by the recent contributions in multiple branches, the first-order splitting algorithms became central for structured nonsmooth optimization. In the large-scale or noisy contexts, when only stochastic information on the smooth part…

Solutions to fractional models inherently exhibit non-smooth behavior, which significantly deteriorates the accuracy and therefore efficiency of existing numerical methods. We develop a two-stage data-infused computational framework for…

Phase field models are promising to tackle various fracture problems where a diffusive crack is introduced and modelled using the phase variable. Owing to the non-convexity of the energy functional, the derived partial differential…

We propose an autonomous quantum error correction scheme using squeezed cat (SC) code against the dominant error source, excitation loss, in continuous-variable systems. Through reservoir engineering, we show that a structured dissipation…

A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…

In this paper, an alternating direction implicit (ADI) difference scheme for two-dimensional time-fractional wave equation of distributed-order with a nonlinear source term is presented. The unique solvability of the difference solution is…

In this paper, we consider a numerical method for the multi-term Caputo-Fabrizio time-fractional diffusion equations (with orders $\alpha_i\in(0,1)$, $i=1,2,\cdots,n$). The proposed method employs a fast finite difference scheme to…

A fast explicit operator splitting (FEOS) method for the molecular beam epitaxy model has been presented in [Cheng, et al., Fast and stable explicit operator splitting methods for phase-field models, J. Comput. Phys., submitted]. The…