Related papers: FDTD: solving 1+1D delay PDE in parallel
The differential equation (DE) with proportional delay is a particular case of the time-dependent delay differential equation (DDE). In this paper, we solve non-linear DEs with proportional delay using the successive approximation method…
This paper is concerned with the decoupling of delayed linear forward-backward stochastic differential equations (D-FBSDEs), which is much more involved than the delay-free case due to the infinite dimension caused by the delay. A new…
The Dirac equation is solved using three-dimensional Finite Difference-Time Domain (FDTD) method. $Zitterbewegung$ and the dynamics of a well-localized electron are used as examples of FDTD application to the case of free electrons.
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
This paper is to investigate if the solution of a hybrid stochastic functional differential equation (SFDE) with infinite delay can be approximated by the solution of the corresponding hybrid SFDE with finite delay. A positive result is…
We propose some multigrid methods for solving the algebraic systems resulting from finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that our multigrid methods are optimal, which means…
We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three…
In this article, we propose numerical scheme for solving a multi-term time-fractional nonlocal parabolic partial differential equation (PDE). The scheme comprises $L2$-$1_{\sigma}$ scheme on a graded mesh in time and Galerkin finite element…
The solvability of a delay differential equation arising in the construction of quadratic cost functionals, i.e. Lyapunov functionals, for a linear time-delay system with a constant and a distributed delay is investigated. We present a…
Monotone finite difference methods provide stable convergent discretizations of a class of degenerate elliptic and parabolic Partial Differential Equations (PDEs). These methods are best suited to regular rectangular grids, which leads to…
Finite time singularity formation in a fourth order nonlinear parabolic partial differential equation (PDE) is analyzed. The PDE is a variant of a ubiquitous model found in the field of Micro-Electro Mechanical Systems (MEMS) and is studied…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
Time-delayed differential equations (TDDEs) are widely used to model complex dynamic systems where future states depend on past states with a delay. However, inferring the underlying TDDEs from observed data remains a challenging problem…
In this contribution the usage of the Parareal method is proposed for the time-parallel solution of the eddy current problem. The method is adapted to the particular challenges of the problem that are related to the differential algebraic…
Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine…
This paper analyzes the accuracy of the standard Yee finite-difference time-domain (FDTD) scheme for simulating normal incidence of harmonic plane waves on planar interfaces between lossless, linear, homogeneous, isotropic media. Unlike…
We compute multiprecision solutions of the Lane-Emden equation. This differential equation arises when introducing the well-known polytropic model into the equation of hydrostatic equilibrium for a nondistorted star. Since such…
Motivated by the idea of imposing paralleling computing on solving stochastic differential equations (SDEs), we introduce a new Domain Decomposition Scheme to solve forward-backward stochastic differential equations (FBSDEs) parallely. We…
A novel efficient and high accuracy numerical method for the time-fractional differential equations (TFDEs) is proposed in this work. We show the equivalence between TFDEs and the integer-order extended parametric differential equations…
We give an exposure to diagrammatic techniques in waveguide QED systems. A particular emphasis is placed on the systems with delayed coherent quantum feedback. Specifically, we show that the $N$-photon scattering matrices in single-qubit…