A Hermite based block method (HBBM) is proposed for the numerical solution of second-
order non-linear elliptic partial differential equations (PDEs). The development of the method …

A computational approach with the aid of the Linear Multistep Method (LMM) for the
numerical solution of differential equations with initial value problems or boundary …

It is difficult to extract weak signals in strong noise background, therefore a piecewise
asymmetric exponential potential under-damped bi-stable stochastic resonance (PAEUBSR) …

A numerical scheme for nonlinear hyperbolic evolution equations is made based on the
implicit Runge-Kutta method and the Fourier spectral method. The detailed discretization …

In this article, we propose novel boundary treatment algorithms to avoid order reduction
when implicit-explicit Runge–Kutta time discretization is used for solving convection …

This paper presents entropy analysis and entropy stable (ES) finite difference schemes for
the reactive Euler equations with chemical reactions. For such equations we point out that …

Abstract In [4], we developed a boundary treatment method for implicit-explicit (IMEX) Runge-
Kutta (RK) methods for solving hyperbolic systems with source terms. Since IMEX RK …

In this paper, the stability analysis and optimal error estimates are presented for a kind of
fully discrete schemes for solving one-dimensional linear convection–diffusion equation with …

When using high-order schemes to solve hyperbolic conservation laws in bounded
domains, it is necessary to properly treat boundary conditions so that the overall accuracy …

In this article, we propose novel boundary treatment algorithms to avoid order reduction
when implicit-explicit Runge-Kutta time discretization is used for solving convection-diffusion …