相关论文: The Trigonometric Cubic B-spline Algorithm for Bur…
The space of $C^1$ cubic Clough-Tocher splines is a classical finite element approximation space over triangulations for solving partial differential equations. However, for such a space there is no B-spline basis available, which is a…
Fault-tolerant quantum computing is a promising technology to solve linear partial differential equations that are classically demanding to integrate. It is still challenging to solve non-linear equations in fluid dynamics, such as the…
N-dimensional B\"acklund transformation (BT), Cole-Hopf transformation and Auto-B\"acklund transformation (Auto-BT) of n-dimensional Burgers system are derived by using simplified homogeneous balance (SHB). By the Auto-BT, another solution…
The advent of isogeometric analysis has prompted a need for methods to generate Trivariate B-spline Solids (TBS) with positive Jacobian. However, it is difficult to guarantee a positive Jacobian of a TBS since the geometric pre-condition…
We announce a new bi-Hamiltonian integrable two-component system admitting the scalar 3rd-order Burgers equation as a reduction.
Component Mode Synthesis methods, such as the Craig-Bampton (CB) approach, are widely used in structural dynamics due to their modularity and compatibility with substructuring workflows. While highly effective for linear systems, extending…
A discrete version of the WKB method is developed and applied to calculate the tunnel splittings between classically degenerate states of spin Hamiltonians. The results for particular model problems are in complete accord with those…
Spatially periodic complex-valued solutions of the Burgers and KdV-Burgers equations are studied in this paper. It is shown that for any sufficiently large time T, there exists an explicit initial data such that its corresponding solution…
In this paper, we present a numerical method, based on iterative Bregman projections, to solve the optimal transport problem with Coulomb cost. This is related to the strong interaction limit of Density Functional Theory. The first idea is…
A theoretical framework for computation of Burgers vectors from strain and lattice rotation data in materials with low dislocation density is presented, as well as implementation into a computer program to automate the process. The efficacy…
Trigonometric and hyperbolic B-splines can be computed via recurrence relations analogous to the classical polynomial B-splines. However, in their original formulation, these two types of B-splines do not form a partition of unity and…
We propose a collocation method based on multivariate polynomial splines over triangulation or tetrahedralization for the numerical solution of partial differential equations. We start with a detailed explanation of the method for the…
In this paper, we propose an efficient numerical scheme for the approximate solution of the time fractional diffusion-wave equation with reaction term based on cubic trigonometric basis functions. The time fractional derivative is…
The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise, which possesses both Burgers-type and cubic nonlinearities. To discretize the…
We investigate the feasibility of modelling turbulence via numeric functional integration. By transforming the Burgers' equation into a functional integral we are able to calculate equal-time spatial correlation of system variables using…
This paper developed a method called "modified exponential cubic B-Spline differential quadrature (mExp-DQM) for space discretization together with a time integration algorithm" for the numerical computation of hyperbolic telegraph equation…
We consider a finite element method with symmetric stabilisation for the discretisation of the transient convection--diffusion equation. For the time-discretisation we consider either the second order backwards differentiation formula or…
We revisit the stochastic collocation method using the exponential of a quadratic spline. In particular, we look in details whether it is more appropriate to fix the ordinates and optimize the abscissae of an interpolating spline or to fix…
We consider the fractional Burgers' equation on $\R^N$ with the critical dissipation term. We follow the parabolic De-Giorgi's method of Caffarelli and Vasseur \cite{Driftdiffusion} and show existence of smooth solutions given any initial…
A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…