Related papers: Invariant compact finite difference schemes
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…
Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…
In this paper, compact finite difference schemes for the modified anomalous fractional sub-diffusion equation and fractional diffusion-wave equation are studied. Schemes proposed previously can at most achieve temporal accuracy of order…
Invariants of general linear system of two hyperbolic partial differential equations (PDEs) are derived under transformations of the dependent and independent variables by real infinitesimal method earlier. Here a subclass of the general…
A general procedure for constructing conservative numerical integrators for time dependent partial differential equations is presented. In particular, linearly implicit methods preserving a time discretised version of the invariant is…
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…
In this paper, a high-order exponential scheme is developed to solve the 1D unsteady convection-diffusion equation with Neumann boundary conditions. The present method applies fourth-order compact exponential difference scheme in spatial…
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…
By combining the ideas of Cartan's equivalence method and the method of the equivariant moving frame for pseudo-groups, we develop an efficient method for solving equivalence problems arising from horizontal Lie pseudo-group actions. The…
In this article, we have developed a higher order compact numerical method for variable coefficient parabolic problems with mixed derivatives. The finite difference scheme, presented here for two-dimensional domains, is based on fourth…
The one-dimensional modified shallow water equations in Lagrangian coordinates are considered. It is shown the relationship between symmetries and conservation laws in Lagrangian coordinates, in mass Lagrangian variables, and Eulerian…
For a system of partial differential equations (PDEs) $F = 0$ admitting a local (point, contact, or higher) symmetry $X$ with the characteristic $\varphi$, invariant solutions satisfy the reduced system $F = \varphi = 0$. We propose a…
This paper is devoted to apply the equivariant moving frame method to study the local equivalence problem of third order ordinarily differential equation under the pseudo-group of fiber preserving transformations.
Several finite difference methods are proposed for the infinitesimal generator of 1D asymmetric $\alpha$-stable L\'{e}vy motions, based on the fact that the operator becomes a multiplier in the spectral space. These methods take the general…
Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to…
Poincare return maps are a fundamental tool for analyzing periodic orbits in hybrid dynamical systems, including legged locomotion, power electronics, and other cyber-physical systems with switching behavior. The Poincare return map…
We propose a geometric numerical analysis of SDEs admitting Lie symmetries which allows us to individuate a symmetry adapted coordinates system where the given SDE has notable invariant properties. An approximation scheme preserving the…
We develop mathematical framework and computational tools for calculating frequency responses of linear time-invariant PDEs in which an independent spatial variable belongs to a compact interval. In conventional studies this computation is…
Invariant finite-difference schemes are considered for one-dimensional magnetohydrodynamics (MHD) equations in mass Lagrangian coordinates for the cases of finite and infinite conductivity. For construction these schemes previously obtained…