We present a new, formally third order, implicit Weighted Essentially NonOscillatory (iWENO3) finite volume scheme for solving systems of nonlinear conservation laws. We then generalize it to define an implicit Eulerian-Lagrangian WENO (iEL-WENO) scheme. Implicitness comes from the use of an implicit Runge-Kutta (RK) time integrator. A specially chosen two-stage RK method allows us to drastical...

From the coordinates transformation, we can see that only after i 1 (ri 1 (t)) is obtained can hi (ri (t )) be obtained. After we obtain hi (ri (t )) ; ~ ij (rj (t )) can be determined from (6). In other words, ~ ij (rj (t )) can not be determined until i 1 (ri 1 (t)) is obtained. However, from the iterative procedure in the main result of [1], we can see that function i 1 (ri 1 (t)) is obtaine...

Strong-stability-preserving (SSP) time-discretization methods have a nonlinear stability property that makes them particularly suitable for the integration of hyperbolic conservation laws. A collection of 4-stage explicit SSP Hermite-Birkhoff methods of orders 4 to 8 with nonnegative coefficients are constructed as k-step analogues of fourth-order Runge-Kutta methods with three off-step points....

In this paper, we analyze implicit-explicit (IMEX) Runge-Kutta (RK) time discretization methods for solving linear convection-diffusion equations. The diffusion operator is treated implicitly via the embedded discontinuous Galerkin (EDG) method and the convection operator explicitly via the upwinding discontinuous Galerkin method.

The aim of this work is to design implicit and semi-implicit high-order well-balanced finite-volume numerical methods for 1D systems balance laws. strategy introduced by two the authors in some previous papers explicit schemes based on application a reconstruction operator applied. property preserved when quadrature formulas are used approximate averages integral source term cells. Concerning t...

Abstract The aim of this work is to apply a semi-implicit (SI) strategy in an implicit-explicit (IMEX) Runge–Kutta (RK) setting introduced Boscarino et al. (J Sci Comput 68:975–1001, 2016) sequence 1D time-dependent partial differential equations (PDEs) with high order spatial derivatives. This gives great flexibility treat these equations, and allows the construction simple linearly implicit s...

Runge-Kutta (RK) pairs are amongst the most popular methods for numerically solving Initial Value Problems. While using an RK pair, we may experience rejection of some steps through interval integration. Traditionally, all evaluations then dropped, and proceed with a completely new round computations. In this work, propose avoiding waste continuing by reusing rejected stages. We focus especiall...

We propose entropy-preserving and entropy-stable partitioned Runge–Kutta (RK) methods. In particular, we extend the explicit relaxation methods to IMEX–RK a class of second-order multirate for stiff problems arising from scale-separable or grid-induced stiffness in system. The proposed approaches not only mitigate system but also fully support entropy-stability properties at discrete level. key...