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, 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(...

This paper establishes a direct method for solving variational problems via a set of Radial basis functions (RBFs) with Gauss-Chebyshev collocation centers. The method consist of reducing a variational problem into a mathematical programming problem. The authors use some optimization techniques to solve the reduced problem. Accuracy and stability of the multiquadric, Gaussian and inverse multiq...

A treecode is presented for evaluating sums defined in terms of the multiquadric radial basis function (RBF), φ(x) = (|x|2 + c2)1/2, where x ∈ R3 and c ≥ 0. Given a set of N nodes, evaluating an RBF sum directly requires CPU time that scales like O(N2). For a given level of accuracy, the treecode reduces the CPU time to O(N logN) using a far-field expansion of φ(x). We consider two options for ...

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...

Radial Basis Function networks with linear output are often used in regression problems because they can be substantially faster to train than Multi-layer Perceptrons. We show how radial base Cauchy, multiquadric and Inverse multiquadric type functions can be used to approximate a rapidly changing continuous test function. In this paper, the performance of the reduced matrix design by QLP decom...

Some researchers have presented the application of radial basis function approximation to the evaluation of option contracts. In a previous study, the authors described the evaluation of Asian options by using radial basis function approximation. The numerical results indicated that the computational accuracy depended on the radial basis function and the reciprocal multi-quadric function was be...