The design and analysis of numerical methods are usually guided by the following:(a) von
Neumann analysis using Fourier series expansion of unknowns,(b) the modified differential …

A new accuracy-preserving parallel algorithm employing compact schemes is presented for
direct numerical simulation of the Navier-Stokes equations. Here the connotation of …

In this paper, we have developed new hybrid compact schemes for the simulation of stream
function–velocity formulation of a two-dimensional incompressible Navier–Stokes equation …

In this paper we propose a novel way to integrate time-evolving partial differential equations
that contain nonlinear advection and stiff linear operators, combining exponential integration …

This paper discusses a new class of optimized implicit-explicit Runge-Kutta methods for the
numerical solution of the dispersive and non-dispersive hyperbolic systems. Optimized …

Deterministic route to turbulence creation in 2D wall boundary layer is shown here by
solving full Navier-Stokes equation by dispersion relation preserving (DRP) numerical …

Accuracy of velocity–vorticity (V→, ω→)-formulations over other formulations in solving
Navier–Stokes equation has been established in recent times. However, the issue of non …

In this article, we have developed a new time-marching method to simulate sound and
soliton propagation in homogeneous and heterogeneous media. The proposed time …

Reaction-diffusion systems are extensively used in the modeling of developmental biology
and in chemical systems to explain the Turing instability are generally highly stiff in both …

This paper derives a new family of implicit–explicit time-marching methods for PDEs with the
second-order derivative in time. The present implicit method is based on the two-derivative …