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The differential transform method (DTM) is a relatively new technique that may be used to find a series solution to differential equations (both linear and nonlinear) through an iterative process. This brief manuscript is an initial effort…
In this paper, spatial modulation (SM) is introduced to layered division multiplexing (LDM) systems for enlarging the spectral efficiency over broadcasting transmission. Firstly, the SM aided LDM (SM-LDM) system is proposed, in which…
We present a new method for solving the Schrodinger equation using the Lossless Transmission Line Model (LTL). The LTL model although extensively used in fiber optics and optical fiber design, it has not yet found application in solid state…
To numerically solve the two-dimensional advection equation, we propose a family of fourth- and higher-order semi-Lagrangian finite volume (SLFV) methods that feature (1) fourth-, sixth-, and eighth-order convergence rates, (2)…
As more and more numerical and analytical solutions to the linear neutron transport equation become available, verification of numerical results is increasingly important. This presentation concerns the development of another benchmark for…
Identifying the discontinuous diffusion coefficient in an elliptic equation with observation data of the gradient of the solution is an important nonlinear and ill-posed inverse problem. Models with total variational (TV) regularization…
In this paper, the use of partitioned linear multistep methods (PLMM) as time integrators for the numerical approximation of some partial differential equations (pdes) is studied. We consider the periodic initial-value problem of two…
This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal…
A recently introduced two-phase flow model by Chun Shen is studied in this work. The model is derived to describe the dynamics of immersed water bubbles in liquid water as carrier. Several assumptions are made to obtain a reduced form of…
We study a class of structured convex optimization problems, which have a two-block separable objective and nonlinear functional constraints as well as affine constraints that couple the two block variables. Such problems naturally arise…
Hamiltonian dynamics of a thin vortex filament in ideal incompressible fluid near a flat fixed boundary is considered at the conditions that at any point of the curve determining shape of the filament the angle between tangent vector and…
The lattice Boltzmann method (LBM) for the variable-coefficient forced Burgers equation (vc-FBE) is studied by choosing the equilibrium distribution and compensatory functions properly. In our model, the vc-FBE is correctly recovered via…
We introduce a method for the fast numerical approximation of linear, second-order parabolic partial differential equations (PDEs for short) with time-independent coefficients based on model order reduction techniques and the Laplace…
With a sufficiently fine discretisation, the Lattice Boltzmann Method (LBM) mimics a second order Crank-Nicolson scheme for certain types of balance laws (Farag et al. [2021]). This allows the explicit, highly parallelisable LBM to…
We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…
In this paper we develop a method to solve evolution equations on Gelfand triples with time-fractional derivative based on monotonicity techniques. Applications include deterministic and stochastic quasi-linear partial differential…
We consider time-harmonic linear elasticity equations in domains containing two-dimensional semi-infinite strips. Since for such problems there exist modes with different signs of group and phase velocity, standard perfectly matched layer…
We consider the numerical solution of the optimal transport problem between densities that are supported on sets of unequal dimension. Recent work by McCann and Pass reformulates this problem into a non-local Monge-Amp\`ere type equation.…
This paper is concerned with an alternative analytical solution of time-fractional nonlinear Schrodinger equation and nonlinear coupled Schrodinger equation obtained by employing fractional reduced differential transform method. The…
Lambert's problem has been long studied in the context of space operations; its solution enables accurate orbit determination and spacecraft guidance. This work offers an analytical solution to Lambert's problem using the Koopman Operator…