this paper presents an operational formulation of the tau method based upon orthogonal polynomials by using a reduced set of matrix operations for the numerical solution of nonlinear multi-order fractional differential equations(fdes). the main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of non-linear algebraic equations....

We study the space discretization of the Cauchy problem for a second order linear parabolic PDE, with one spatial dimension and unbounded time and space-dependent coefficients. The PDE free term and the initial data are also allowed to grow. Under the assumption that the PDE does not degenerate, the problem’s weak solution is approximated in space, with finite-difference methods. The rate of co...

The problem of a stationary generalized convective flow modelling bioconvection is considered. The viscosity is assumed to be a function of the concentration of the micro-organisms. As a result the PDE system describing the bioconvection model is quasilinear. The existence and uniqueness of the weak solution of the PDE system is obtained under minimum regularity assumption on the viscosity. Num...

We introduce a novel numerical method for a recently developed perspective Shape-from-Shading model. In order to discretise the corresponding partial differential equation (PDE), Prados et al. employed the dynamical programming principle yielding a Hamilton-Jacobi-Bellman equation. We reduce that model to its essential, namely to the underlying Hamilton-Jacobi equation. For this PDE, we propose...

In this work the stability properties of a nonlinear partial differential equation (PDE) with state-dependent parameters is investigated. Among other things, the PDE describes freezing of foodstuff, and is closely related to the (Potential) Burgers’ Equation. We show that for certain forms of coefficient functions, the PDE converges to a stationary solution given by (fixed) boundary conditions ...

In this paper, the fractional Sturm-Liouville problems, in which the second order derivative is replaced by a fractional derivative, are derived by the Homotopy perturbation method. The fractional derivatives are described in the Caputo sense. The present results can be implemented on the numerical solutions of the fractional diffusion-wave equations. Numerical results show that HPM is effectiv...

We develop a spectrally accurate numerical method to compute solutions of a model PDE used in plasma physics to describe diffusion in velocity space due to Fokker–Planck collisions. The solution is represented as a discrete and continuous superposition of normalizable and nonnormalizable eigenfunctions via the spectral transform associated with a singular Sturm–Liouville operator. We present a ...

Numerical and asymptotic results are presented for a coupled PDE system that models recent experiments of the selffocussing of laser light in a nematic liquid crystal. This study complements previous asymptotic analyses which, in a narrow-beam limit, describe two essential features observed in nematic self-focussing the undulation and filamentation of a laser beam. These numerical computations ...

New General Ray (GR) method for solution of the Dirichlet boundary value problem for the class of elliptic Partial Differential Equations (PDE) is proposed. GRmethod consists in application of the Radon transform directly to the PDE and in reduction PDE to assemblage of Ordinary Differential Equations (ODE). The class of the PDE includes the Laplace, Poisson and Helmgoltz equations. GRmethod pr...

this paper concerns the problem of robust stabilization of uncertain fractional-order non-autonomous systems. in this regard, a single input active control approach is proposed for control and stabilization of three-dimensional uncertain fractional-order systems. the robust controller is designed on the basis of fractional lyapunov stability theory. furthermore, the effects of model uncertainti...