Variational formulation and projectional methods for the second order transport equation

On Fuzzy Solution for Exact Second Order Fuzzy Differential Equation

In the present paper, the analytical solution for an exact second order fuzzy initial value problem under generalized Hukuhara differentiability is obtained. First the solution of first order linear fuzzy differential equation under generalized Hukuhara differentiability is investigated using integration factor methods in two cases. The second based on the type of generalized Hukuhara different...

Spectral methods for the wave equation in second-order form

Current spectral simulations of Einstein’s equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudospectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on ...

Variational Formulation of Problems and Variational Methods

An Application of Variational Methods to Second-order Impulsive Differential Equation with Derivative Dependence

In this article, we study the existence of solutions for nonlinear impulsive problems. We show the existence of classical solutions by using variational methods.

A Fourth Order Accurate Finite Difference Scheme for the Elastic Wave Equation in Second Order Formulation

We present a fourth order accurate finite difference method for the elastic wave equation in second order formulation, where the fourth order accuracy holds in both space and time. The key ingredient of the method is a boundary modified fourth order accurate discretization of the second derivative with variable coefficient, (μ(x)ux)x. This discretization satisfies a summation by parts identity ...