We present Helmholtz or Helmholtz like equations for the approximation of the timeharmonic wave propagation in gases with small viscosity, which are completed with local boundary conditions on rigid walls. We derived approximative models based on the method of multiple scales for the pressure and the velocity separately, both up to order 2. Approximations to the pressure are described by the He...

Algorithms for the solution of symmetric diagonally dominant tridiagonal systems of linear equations with constant diagonals are considered. Such systems occur, for example, when solving certain constant-coecient elliptic partial diierential equations by the Fourier method. In particular, the specialized LU factorization method of Malcolm and Palmer (SpLU), the cyclic reduction method of Hockne...

The nonlinear dynamic response of thin plates made of linear viscoelastic material of fractional derivative type is investigated. The resulting governing equations are three coupled nonlinear fractional partial differential equations in terms of displacements. The solution is achieved using the AEM. According to this method the original equations are converted into three uncoupled linear equati...

We describe a hybrid method based on the combined use of the Fourier Galerkin and finite-volume techniques to solve the fluid dynamics equations in cylindrical geometries. A Fourier expansion is used in the angular direction, partially translating the problem to the Fourier space and then solving the resulting equations using a finite-volume technique. We also describe an algorithm required to ...

in this paper, we present an efficient method for determining the solution of the stochastic second kind volterra integral equations (svie) by using the taylor expansion method. this method transforms the svie to a linear stochastic ordinary differential equation which needs specified boundary conditions. for determining boundary conditions, we use the integration technique. this technique give...

We establish an abstract infinite dimensional KAM theorem dealing with unbounded perturbation vector-field, which could be applied to a large class of Hamiltonian PDEs containing the derivative ∂x in the perturbation. Especially, in this range of application lie a class of derivative nonlinear Schrödinger equations with Dirichlet boundary conditions and perturbed Benjamin-Ono equation with peri...

We prove that higher Sobolev norms of solutions of quasi-linear Klein-Gordon equations with small Cauchy data on S remain small over intervals of time longer than the ones given by local existence theory. This result extends previous ones obtained by several authors in the semi-linear case. The main new difficulty one has to cope with is the loss of one derivative coming from the quasi-linear c...

The undamped wave equation on an open domain of arbitrary dimension and boundary of class C 1 is considered. On parts of the boundary the normal derivative of the solution equals the convolution of its time derivative with a measure of positive type. This setting subsumes standard disssipative boundary conditions as well as the interaction with vis-coelastic boundary materials. Applying methods...

This study aimed at linear stability analysis of the stratified two-phase liquid-gas flow in a horizontal pipe. First, equations governing the linear stability of flow in each phase and boundary conditions were obtained. The governing equations were eigenvalue Orr Sommerfeld equations which are difficult and stiff problems to solve. After obtaining the velocity profiles of the gas and liquid ph...

This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady state solutions. Absorbing and reflecting boundary conditions are considered, and illustrated through several examples. Reflecting boundary conditions involv...