On the Stability of One-Dimensional Wave Equation

On the Stability of One-Dimensional Wave Equation

We prove the generalized Hyers-Ulam stability of the one-dimensional wave equation, u(tt) = c(2)u(xx), in a class of twice continuously differentiable functions.

NUMERICAL SOLUTION OF ONE-DIMENSIONAL HEAT AND WAVE EQUATION BY NON-POLYNOMIAL QUINTIC SPLINE

This paper present a novel numerical algorithm for the linear one-dimensional heat and wave equation. In this method, a nite dierenceapproach had been used to discrete the time derivative while cubic spline isapplied as an interpolation function in the space dimension. We discuss theaccuracy of the method by expanding the equation based on Taylor series andminimize the error. The proposed metho...

Some new exact traveling wave solutions one dimensional modified complex Ginzburg- Landau equation

‎In this paper‎, ‎we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-‎dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method‎, homogeneous balance method, extended F-expansion method‎. ‎By ‎using homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by j...

Travelling Wave Solutions of the One Dimensional Diffusion-reaction Equation

Optimal observation of the one-dimensional wave equation

In this paper, we consider the homogeneous one-dimensional wave equation on [0, π] with Dirichlet boundary conditions, and observe its solutions on a subset ω of [0, π]. Let L ∈ (0, 1). We investigate the problem of maximizing the observability constant, or its asymptotic average in time, over all possible subsets ω of [0, π] of Lebesgue measure Lπ. We solve this problem by means of Fourier ser...