*Correspondence: [email protected] Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran Abstract In this paper, we solve a time-space fractional diffusion equation. Our methods are based on normalized Bernstein polynomials. For the space domain, we use a set of normalized Bernstein polynomials and for the time domain, which is a semi-infinite domain, ...

Some difficulties emerging during the construction of fuzzy rule bases are inherited from the type of the applied fuzzy reasoning. In fuzzy systems, when classical methods (e.g. the Compositional Rule of Inference) are applied, the completeness of the fuzzy rule base is required to generate meaningful output. This means, that the fuzzy rule base has to cover all possible inputs. The way of buil...

Petroleum reservoir modelling requires effective multiscale methods for the numerical simulation of two-phase flow in porous media. This paper proposes the application of a novel meshfree particle method to the Buckley-Leverett model. The utilized meshfree advection scheme, called AMMoC, is essentially a method of characteristics, which combines an adaptive semi-Lagrangian method with local mes...

In this report, a charge preserving numerical resolution of the 1D Vlasov-Ampère equation is achieved, with a forward Semi-Lagrangian method introduced in [10]. The Vlasov equation belongs to the kinetic way of simulating plasmas evolution, and is coupled with the Poisson’s equation, or equivalently under charge conservation, the Ampère’s one, which self-consistently rules the electric field ev...

In this paper, we construct a semi-discrete scheme and a fully discrete scheme using the Wilson nonconforming element for the parabolic integro-differential equation arising in modeling the non-Fickian flow in porous media by the interior penalty method. Without using the conventional elliptic projection, which was an indispensable tool in the convergence analysis of finite element methods in p...

Previous work on nonrigid registration of medical images based on thin plate splines has concentrated on using interpolation schemes Such schemes force the corresponding land marks to exactly match each other and thus assume that the landmark positions are known exactly However in real applications the localization of landmarks is always prone to error Therefore to cope with these errors we hav...

We present a parallel algorithm for solving the 4D Vlasov equation. Our algorithm is designed for distributed memory architectures. It uses an adaptive numerical method which reduces computational cost. This adaptive method is a semi-Lagrangian scheme based on hierarchical finite elements. It involves a local interpolation operator. Our algorithm handles both irregular data dependencies and the...

This paper presents two methods for solving the four-dimensional Vlasov equation on a grid of the phase space. The two methods are based on the semi-Lagrangian method which consists in computing the distribution function at each grid point by following the characteristic curve ending there. The first method reconstructs the distribution function using local splines which are well suited for a p...