Related papers: Fundamental Schemes for Efficient Unconditionally …
Fourier-domain Difference Map (FDM) for phase retrieval with two oversampled coded diffraction patterns are proposed. FDM is a 3-parameter family of fixed point algorithms including Fourier-domain Hybrid-Projection-Reflection (FHPR) and…
In this paper we propose an explicit two-level conservative scheme based on a TE/TM like splitting of the field components in time. Its dispersion properties are adjusted to accelerator problems. It is simpler and faster than the implicit…
This paper presents a novel implicit scheme for the constraint resolution in real-time finite element simulations in the presence of contact and friction. Instead of using the standard motion correction scheme, we propose an iterative…
Multidimensional population balance models (PBMs) describe chemical and biological processes having a distribution over two or more intrinsic properties (such as size and age, or two independent spatial variables). The incorporation of…
Safe and economic operation of networked systems is often challenging. Optimization-based schemes are frequently considered, since they achieve near-optimality while ensuring safety via the explicit consideration of constraints. In…
In this paper, we consider the finite difference method for the generalized two-dimensional (2D) multi-term time-fractional Oldroyd-B fluid model, which is a subclass of non-Newtonian fluids. Different from the general multi-term time…
The Residual Smooting Scheme (RSS) have been introduced in \cite{AverbuchCohenIsraeli} as a backward Euler's method with a simplified implicit part for the solution of parabolic problems. RSS have stability properties comparable to those of…
Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for…
In this paper, an improvement of the finite difference time domain (FDTD) method using a non-standard finite difference scheme is presented. The standard numerical scheme for the second derivative in the spatial domain is replaced by a…
In this note we propose and analyze novel implicit-explicit methods based on second order strong stability preserving multistep time discretizations. Several schemes are developed, and a linear stability analysis is performed to study their…
This work establishes a comprehensive analytical framework for studying implicit fractional differential systems with distributed memory and time delays. We develop novel fractional integral inequalities of Gr\"onwall--Wendroff type that…
This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence may exhibit instabilities similar to those of the base…
The implicit compact finite-difference scheme was developed for evolutionary partial differential parabolic and Schr\"odinger-type equations and systems with a weak nonlinearity. To make a temporal step of the compact implicit scheme we…
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different…
We propose a new deep learning algorithm for solving high-dimensional parabolic integro-differential equations (PIDEs) and forward-backward stochastic differential equations with jumps (FBSDEJs). This novel algorithm can be viewed as an…
Stability and convergence analysis for the domain decomposition finite element/finite difference (FE/FD) method is presented. The analysis is designed for semi-discrete finite element scheme for the time-dependent Maxwell's equations. The…
This paper presents a novel methodology for fast simulation and analysis of transient heat transfer. The proposed methodology is suitable for real-time applications owing to (i) establishing the solution method from the viewpoint of…
Two semi-implicit Euler schemes for differential inclusions are proposed and analyzed in depth. An error analysis shows that both semi-implicit schemes inherit favorable stability properties from the differential inclusion. Their…
In the past decades, the finite difference methods for space fractional operators develop rapidly; to the best of our knowledge, all the existing finite difference schemes, including the first and high order ones, just work on uniform…
In this study we explore a new simulation scheme for partial differential equations known as Information Field Dynamics (IFD). Information field dynamics attempts to improve on existing simulation schemes by incorporating Bayesian field…