Weighted compact nonlinear schemes (WCNS) are a family of nonlinear shock capturing
schemes that are suitable for solving problems with discontinuous solutions. The schemes …

This paper proposes a high-order pseudo arc-length method (PALM) for multi-medium flows
with strong robustness, stability, and positivity preservation for solving one-and two …

Finite Difference schemes are the amongst the most popular discretization methods for
obtaining numerical solutions to the Navier–Stokes equations. Their versatility at handling …

In this paper, we construct a family of temporal high-order parametric relaxation Runge–
Kutta (pRRK) schemes for stiff ordinary differential equations (ODEs), and explore their …

Hyperbolic conservation law equation is a system of partial differential equations, which has
the characteristics of hyperbolic type, and its solution will eventually evolve into a singular …

A seventh-order accurate high-resolution compact nonlinear scheme is developed based on
the fifth-order scheme, TCNS-II (Zhang et al., 2019), such that the stencil used for the …

A hyperbolic conservation equation can easily generate strong discontinuous solutions such
as shock waves and contact discontinuity. By introducing the arc-length parameter, the …

In this paper, we study the numerical solution for the evolutionary stable distribution (ESD)
model. A new implicit–explicit scheme is proposed to discretize the ESD model, which can …

In inland fisheries, transporting fishery resource individuals from a habitat to spatially apart
habitat (s) has recently been considered for fisheries stock management in the natural …

This paper proposes a high-order maximum-principle-preserving (MPP) conservative
scheme for convection-dominated diffusion equations. For high-order spatial discretization …