and Applied Analysis 3 with the initial conditions

In this paper we consider hyperbolic initial value problems subject to periodic boundary conditions with nonsmooth data. We show that if we filter the data and solve the problem by the Galerkin-Collocation method, recently proposed by us, then we can recover pointwise values with spectral accuracy, provided that the actual solution is piecewise smooth. For this we have to perform a local smooth...

An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting nonlinear equation is solved via the Petviashvili iterative scheme. The computational results are compared to some existing approaches, such as Tanaka’s method and...

The Fourier pseudo-spectral method has been studied for a onedimensional coupled system of viscous Burgers equations. Two test problems with known exact solutions have been selected for this study. In this paper, the rate of convergence in time and error analysis of the solution of the first problem has been studied, while the numerical results of the second problem obtained by the present meth...

In this paper, a sixth order energy-conserved method is proposed for solving the three-dimensional time-domain Maxwell’s equations. Based on the method of lines, the spatial derivatives of the Maxwell’s equations are approximated with the aid of Fourier pseudo-spectral methods. The resulting ordinary differential equations can be cast as a canonical Hamiltonian system. Then, a fully-discretized...

In the present study, a spectral finite element method is developed for free and forced transverse vibration of Levy-type moderately thick rectangular orthotropic plates based on first-order shear deformation theory. Levy solution assumption was used to convert the two-dimensional problem into a one-dimensional problem. In the first step, the governing out-of-plane differential equations are tr...

in the present study, a spectral finite element method is developed for free and forced transverse vibration of levy-type moderately thick rectangular orthotropic plates based on first-order shear deformation theory. levy solution assumption was used to convert the two-dimensional problem into a one-dimensional problem. in the first step, the governing out-of-plane differential equations are tr...

This paper discusses about the solution of fuzzy Volterra integral equation of first-kind (F-VIE1) using spectral method. The parametric form of fuzzy driving term is applied for F-VIE1, then three classifications for (F-VIE1) are searched to solve them. These classifications are considered based on the interval sign of the kernel. The Gauss-Legendre points and Legendre weights for arithmetics ...