ACCURATE NUMERICAL SOLUTIONS FOR NONLINEAR WAVES

Accurate and efficient numerical solutions for elliptic obstacle problems

Elliptic obstacle problems are formulated to find either superharmonic solutions or minimal surfaces that lie on or over the obstacles, by incorporating inequality constraints. In order to solve such problems effectively using finite difference (FD) methods, the article investigates simple iterative algorithms based on the successive over-relaxation (SOR) method. It introduces subgrid FD method...

Exact and numerical solutions for nonlinear differential equation of Jeffrey-Hamel flow

Theoretical and Numerical Solutions of Linear and Nonlinear Elastic Waves in a Thin Rod

In this paper, we report theoretical and numerical solutions of linear and nonlinear elastic waves in a thin rod. First, the classical solution of linear elastic wave in a thin rod is adapted such that it is ready to be compared with the numerical solution of a nonlinear formulation. Based on mass and momentum conservation, we then derive several forms of modeling equations for nonlinear elasti...

Dromion solutions for nonlinear electron acoustic waves in space plasmas

Recent high resolution measurements of POLAR and FAST satellites have revealed two-dimensional coherent structures in the polar cap boundary layer (PCBL) region. Since the ion temperature is often observed to be greater than the electron temperature in this region, electron acoustic waves can exist as a normal mode of the plasma system. It is shown that the nonlinear evolution of such waves can...

Numerical Verifications of Solutions for Nonlinear Hyperbolic Equations

In this paper, we consider a numerical technique to enclose the solutions with guaranteed error bounds for nonlinear hyperbolic initial boundary value problems as well as to verify the existence of solutions. Using a finite element approximation and explicit error estimates for a certain simple linear hyperbolic problem, we construct, by computer, a set of functions which satisfies the conditio...