Space-fractional Wave Equation Research Articles

A weighted numerical algorithm for two and three dimensional two-sided space fractional wave equations

A weighed numerical scheme that can effectively solve the fractional wave equation in a finite domain is provided. We focus on detailedly discussing the two and three dimensional two-sided space fractional wave equations with homogeneous boundary conditions. A second order finite difference scheme is used to discretize the space fractional derivative and the time derivative. Additionally, the numerical results confirm that the weighted numerical algorithm is convergent with second order accuracy in both space and time directions for the homogeneous boundary fractional problems.

Error Analysis of An Explicit Finite Difference Approximation for the Space Fractional Wave Equations

In this paper, the space fractional wave equation (SFWE) is numerically studied, where the fractional derivative is defined in the sense of Caputo. An explicit finite difference approximation (EFDA) for SFWE is presented. The stability and the error analysis of the EFDA are discussed. To demonstrate the effectiveness of the approximated method, some test examples are presented.

Fractional calculus approach to the acoustic wave propagation with space-dependent sound speed

In this note we study the space-fractional wave equation in relation to the propagation of acoustic waves with space-dependent sound speed. We take into account this variability, by using the space-fractional derivative in the classical wave equation. In order to give a clear comprehension of this mathematical formulation, we discuss the analytic solution of a simple boundary value problem (BVP) by an operational method, finding a fractional oscillating spatial profile.

Numerical solution of two-sided space-fractional wave equation using finite difference method

In this paper, a class of finite difference method for solving two-sided space-fractional wave equation is considered. The stability and consistency of the method are discussed by means of Gerschgorin theorem and using the stability matrix analysis. Numerical solutions of some wave fractional partial differential equation models are presented. The results obtained are compared to exact solutions.