Variational iteration method has been extensively employed to deal with linear and
nonlinear differential equations of integer and fractional order. The key property of the …

In current study, the modified variational iteration algorithm-I is investigated in the form of the
analytical and numerical treatment of different types of nonlinear partial differential …

High-order entropy-stable discontinuous Galerkin methods for the compressible Euler and
Navier-Stokes equations require the positivity of thermodynamic quantities in order to …

For time-dependent PDEs, the numerical schemes can be rendered bound-preserving
without losing conservation and accuracy by a postprocessing procedure of solving a …

In this paper, we are interested in constructing a scheme solving compressible Navier–
Stokes equations, with desired properties including high order spatial accuracy …

In this work we introduce semi-implicit or implicit finite difference schemes for the continuity
equation with a gradient flow structure. Examples of such equations include the linear …

We consider solving a generalized Allen-Cahn equation coupled with a passive convection
for a given incompressible velocity field. The numerical scheme consists of the first order …

In this paper, we construct bound-preserving interior penalty discontinuous Galerkin (IPDG)
methods with a second-order implicit pressure explicit concentration (SIPEC) time marching …

We show that the classical fourth order accurate compact finite difference scheme with high
order strong stability preserving time discretizations for convection diffusion problems …

An early warning model for simulating conventional sudden water pollution in a plain river
network based on a mainstream algorithm is first developed, and a calculation method for …