Ground water pollution is a serious environmental problem that may damage human health, destroy the ecosystem and cause water shortage. In all situations, we need tool to predict the pollutant distribution in ground water. The only tool that we can use is mathematical modeling. Recently, very intensive efforts have been devoted to develop meshless or element free methods that eliminate the need...

The average diffusion propagator (ADP) obtained from diffusion MRI (dMRI) data encapsulates important structural properties of the underlying tissue. Measures derived from the ADP can be potentially used as markers of tissue integrity in characterizing several mental disorders. Thus, accurate estimation of the ADP is imperative for its use in neuroimaging studies. In this work, we propose a sim...

Madych and Nelson(1990) proved Multiquadric (MQ) mesh-independent Radial Basis Functions (RBFs) enjoy exponential convergence. The primary disadvantage of the MQ scheme is that it is global, hence the coe cient matrices obtained from this discretization scheme are full. Full matrices tend to become progressively more ill-conditioned as the rank increases. In this paper, we explore several techn...

Newton iteration is a standard tool for the numerical solution of nonlinear partial diierential equations. We show how globally supported multiquadric radial basis functions can be used for this task. Some experiments with Nash iteration are also included.

In this paper, we are interested in some convergent formulations for the unsymmetric collocation method or the so-called Kansa’s method. We review some newly developed theories on solvability and convergence. The rates of convergence of these variations of Kansa’s method are examined and verified in arbitrary–precision computations. Numerical examples confirm with the theories that the modified...

In this paper, the conventional level set methods are extended as an effective approach for shape and topology optimization by the introduction of the radial basis functions (RBFs). The RBF multiquadric splines are used to construct the implicit level set function with a high level of accuracy and smoothness and to discretize the original initial value problem into an interpolation problem. The...

In this paper, the aim is to solve the neutral delay differential equations in the following form using multiquadric approximation scheme, (1){ y′(t) = f(t, y(t), y(t− τ(t, y(t))), y′(t− σ(t, y(t)))), t1 ≤ t ≤ tf , y(t) = φ(t), t ≤ t1, where f : [t1, tf ] × R × R × R → R is a smooth function, τ(t, y(t)) and σ(t, y(t)) are continuous functions on [t1, tf ]×R such that t−τ(t, y(t)) < tf and t− σ(...

Multiquadric method is employed for solving the two dimensional depth-integrated water quality model and the eutrophication model in marine environments. The models simulate the spatial and temporal variations of nutrients in the Tolo Harbour of Hong Kong by taking considerations of the tidal current, wind stress, growth dynamics of phytoplankton and the transformation rate of nutrients. The ph...