In this work, we present a family of time and space high order finite volume schemes for the solution full Boltzmann equation. The velocity is approximated by using discrete ordinate approach while collisional integral spectral methods. reconstruction implemented integrating distribution function, which describes state system, over arbitrarily shaped closed control volumes Central Weighted ENO ...

The space-time geometric structure of Maxwell’s equations is examined and a subset of them is found to define a pair of exact discrete time-stepping relations. The desirability of adopting an approach to the discretization of electromagnetic problems which exploits this fact is advocated, and the name topological time-stepping for numerical schemes complying with it is suggested. The analysis o...

In this paper we propose a wavelet Taylor–Galerkin method for the numerical solution of time-dependent advection–di usion problems. The discretization in time is performed before the spatial discretization by introducing secondand third-order accurate generalization of the standard time stepping schemes with the help of Taylor series expansions in time step. Numerical schemes taking advantage o...

Two-fluid ideal plasma equations are a generalized form of the ideal MHD equations in which electrons and ions are considered as separate species. The design of efficient numerical schemes for the these equations is complicated on account of their non-linear nature and the presence of stiff source terms, especially for high charge to mass ratios and for low Larmor radii. In this article, we des...

In this paper, we propose wavelet Taylor–Galerkin schemes for parabolic and hyperbolic PDEs taking full advantage of the compression properties of wavelet basis. The discretization in time is performed before the spatial discretization by introducing high-order generalization of the standard time-stepping schemes with the help of Taylor series expansion in time step. Then, we present numerical ...

In this paper we present an implicit time-stepping scheme for multibody systems with intermittent contact by incorporating the contact constraints as a set of complementarity and algebraic equations within the dynamics model. Two primary sources of stability and accuracy problems in prior time stepping schemes for differential complementarity models of multibody systems are the use of polyhedra...

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problem...

Implicit time stepping is often difficult to parallelize. The recently proposed Minimal Residual Approximate Implicit (MRAI) schemes [2] are specially designed as a cheaper and parallelizable alternative for implicit time stepping. A several GMRES iterations are performed to solve approximately the implicit scheme of interest, and the step size is adjusted to guarantee stability. A natural way ...

An approach for constructing high-order Discontinuous Galerkin schemes which preserve discrete conservation in the presence of arbitrary mesh motion, and thus obey the GCL, is derived. The approach is formulated for the most general case where only the coordinates defining the mesh elements are known at discrete locations in time, and results in the prescription of higher-order quadrature rules...