Dynamic von-Kármán plate models consist of three coupled non-linear, time-dependent partial differential equations. These equations have been recently solved numerically [Kirby, R., Yosibash, Z., 2004. Solution of von-Kármán dynamic non-linear plate equations using a pseudo-spectral method. Comp. Meth. Appl. Mech. Eng. 193 (6–8) 575–599 and Yosibash, Z., Kirby, R., Gottlieb, D., 2004. Pseudo-sp...

A volume penalization approach to simulate magnetohydrodynamic (MHD) flows in confined domains is presented. Here the incompressible visco-resistive MHD equations are solved using parallel pseudo-spectral solvers in Cartesian geometries. The volume penalization technique is an immersed boundary method which is characterized by a high flexibility for the geometry of the considered flow. In the p...

In this paper, we develop, analyze and test the Fourier spectral methods for solving the Degasperis–Procesi (DP) equation which contains nonlinear high order derivatives, and possibly discontinuous or sharp transition solutions. The L2 stability is obtained for general numerical solutions of the Fourier Galerkin method and Fourier collocation (pseudospectral) method. By applying the Gegenbauer ...

Numerical simulations of phase-field models require long time computations and therefore it is necessary to develop efficient and highly accurate numerical methods. In this paper, we propose fast and stable explicit operator splitting methods for both oneand two-dimensional nonlinear diffusion equations for thin film epitaxy with slope selection and Cahn-Hilliard equation. The equations are spl...

to control the nonlinear numerical instability, throughout the time evolution of the eulerian form of the nonlinear rotating shallow water equations, it is necessary to add numerical diffusion to the solution. it is clear that, this extra numerical diffusion degrades the accuracy of the numerical solution and should be kept as small as possible. in a conventional approach a hyper-diffusion is u...

In this paper, a Bernoulli pseudo-spectral method for solving nonlinear fractional Volterra integro-differential equations is considered. First existence of a unique solution for the problem under study is proved. Then the Caputo fractional derivative and Riemman-Liouville fractional integral properties are employed to derive the new approximate formula for unknown function of the problem....

The rapid developments of artificial intelligence in the last decade are influencing aerospace engineering to a great extent and research this context is proliferating. In paper, trajectory optimization three-stage launch vehicle powering phase subject sun-synchronous orbit considered. To solve optimal control problem, Gauss pseudo-spectral method (GPM) used transform model nonlinear programming ...