When using high-order schemes to solve hyperbolic conservation laws in bounded domains, it is necessary properly treat boundary conditions so that the overall accuracy and stability are maintained. In [1, 2] a finite difference treatment method proposed for Runge-Kutta methods of laws. The combines an inverse Lax-Wendroff procedure WENO type extrapolation achieve desired stability. this paper, ...

Abstract We study the following wave equation $$u_{tt}-\Delta u+\alpha (t)\left| u_{t}\right| ^{m(\cdot )-2}u_{t}=0$$ u tt - Δ + α ( t ) <mm...

We present a new family of high-order shock-capturing finite difference numerical methods for systems conservation laws. These methods, called Adaptive Compact Approximation Taylor (ACAT) schemes, use centered $(2p + 1)$-point stencils, where $p$ may take values in $\{1, 2, \dots, P\}$ according to smoothness indicators the stencils. The are based on combination robust first order scheme and Ap...

The algebraic flux correction (AFC) schemes presented in this work constrain a standard continuous finite element discretization of nonlinear hyperbolic problem to satisfy relevant maximum principles and entropy stability conditions. desired properties are enforced by applying limiter antidiffusive fluxes that represent the difference between high-order baseline scheme property-preserving appro...

Abstract Conservation properties of iterative methods applied to implicit finite volume discretizations nonlinear conservation laws are analyzed. It is shown that any consistent multistep or Runge-Kutta method globally conservative. Further, it Newton’s method, Krylov subspace and pseudo-time iterations conservative while the Jacobi Gauss-Seidel not in general. If using an explicit a locally di...

Abstract A quasi–second-order scheme is developed to obtain approximate solutions of the two-dimensional shallow water equations (SWEs) with bathymetry. The based on a staggered finite volume space discretization: scalar unknowns are located in discretization cells while vector edges mesh. monotonic upwind-central for conservation laws (MUSCL)-like interpolation discrete convection operators he...

Based on the recent development of Jacobian-free Lax–Wendroff (LW) approaches for solving hyperbolic conservation laws (Zorio et al. in J Sci Comput 71:246–273, 2017, Carrillo and Parés 80:1832–1866, 2019), a novel collection explicit multistage multiderivative solvers is presented this work. In contrast to Taylor time-integration methods, Runge–Kutta (MDRK) techniques achieve higher-order cons...