Radial Basis Function (RBF) methods that employ infinitely differentiable basis functions featuring a shape parameter are theoretically spectrally accurate methods for scattered data interpolation and for solving Partial Differential Equations. It is also theoretically known that RBF methods are most accurate when the linear systems associated with the methods are extremely ill-conditioned. Thi...

Keywords: Volterra integro-differential equations Multistep collocation Superconvergence Stability a b s t r a c t Multistep collocation methods for Volterra integro-differential equations are derived and analyzed. They increase the order of convergence of classical one-step collocation methods, at the same computational cost. The numerical stability analysis is carried out and classes of A 0-s...

In this paper, collocation methods are used for detecting blow-up solutions of nonlinear homogeneous Volterra-Hammerstein integral equations. To do this, we introduce the concept of “blow-up collocation solution” and analyze numerically some blow-up time estimates using collocation methods in particular examples where previous results about existence and uniqueness can be applied. Finally, we d...

This study proposes RBF Network hybrid learning with Particle Swarm Optimization for better convergence, error rates and classification results. In conventional RBF Network structure, different layers perform different tasks. Hence, it is useful to split the optimization process of hidden layer and output layer of the network accordingly. RBF Network hybrid learning involves two phases. The fir...

Abstract. A local convergence rate is established for an orthogonal collocation method based on Radau quadrature applied to an unconstrained optimal control problem. If the continuous problem has a sufficiently smooth solution and the Hamiltonian satisfies a strong convexity condition, then the discrete problem possesses a local minimizer in a neighborhood of the continuous solution, and as the...

This paper presents an axiomatic approach for constructing radial basis function (RBF) neural networks. This approach results in a broad variety of admissible RBF models, including those employing Gaussian RBF's. The form of the RBF's is determined by a generator function. New RBF models can be developed according to the proposed approach by selecting generator functions other than exponential ...

A novel particle swarm optimisation (PSO) tuned radial basis function (RBF) network model is proposed for identification of non-linear systems. At each stage of orthogonal forward regression (OFR) model construction process, PSO is adopted to tune one RBF unit’s centre vector and diagonal covariance matrix by minimising the leave-one-out (LOO) mean square error (MSE). This PSO aided OFR automat...

Dautzenberg M, Kahnert A, Stasch JP, Just A. Role of soluble guanylate cyclase in renal hemodynamics and autoregulation in the rat. Am J Physiol Renal Physiol 307: F1003–F1012, 2014. First published September 10, 2014; doi:10.1152/ajprenal.00229.2014.—We studied the influence of soluble guanylate (sGC) on renal blood flow (RBF), glomerular filtration rate (GFR), and RBF autoregulation and its r...

this paper extends the sequential learning algorithm strategy of two different types of adaptive radial basis function-based (rbf) neural networks, i.e. growing and pruning radial basis function (gap-rbf) and minimal resource allocation network (mran) to cater for on-line identification of non-linear systems. the original sequential learning algorithm is based on the repetitive utilization of s...

We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a collocation problem, and we give some examples ...