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An adaptive pseudospectral method is presented for solving a class of multiterm fractional boundary value problems (FBVP) which involve Caputo-type fractional derivatives. The multiterm FBVP is first converted into a singular Volterra integrodifferential equation (SVIDE). By dividing the interval of the problem to subintervals, the unknown function is approximated using a piecewise interpolation polynomial with unknown coefficients which is based on shifted Legendre-Gauss (ShLG) collocation points. Then the problem is reduced to a system of algebraic equations, thus greatly simplifying the problem. Further, some additional conditions are considered to maintain the continuity of the approximate solution and its derivatives at the interface of subintervals. In order to convert the singular integrals of SVIDE into nonsingular ones, integration by parts is utilized. In the method developed in this paper, the accuracy can be improved either by increasing the number of subintervals or by increasing the degree of the polynomial on each subinterval. Using several examples including Bagley-Torvik equation the proposed method is shown to be efficient and accurate.

We study the numerical solutions to semi-infinite-domain two-point boundary value problems and initial value problems. A smooth, strictly monotonic transformation is used to map the semiinfinite domain x ∈ 0, ∞ onto a half-open interval t ∈ −1, 1. The resulting finite-domain twopoint boundary value problem is transcribed to a system of algebraic equations using Chebyshev-Gauss CG collocation, while the resulting initial value problem over a finite domain is transcribed to a system of algebraic equations using Chebyshev-Gauss-Radau CGR collocation. In numerical experiments, the tuning of the map φ : −1, 1 → 0, ∞ and its effects on the quality of the discrete approximation are analyzed.

Artículo de publicación ISIThis work deals with the joint simulation of copper grade (as a continuous regionalized variable) and rock type (as a categorical variable) in Lince–Estefanía deposit, located in northern Chile. The region under study is heterogeneous, containing three main rock types (intrusive, andesite and breccia bodies) with different copper grade distributions. To perform joint simulation, themulti-Gaussian and pluri- Gaussian models are used in a combined form. To this end, three auxiliary Gaussian random fields are considered, one for simulating copper grade, up to a monotonic transformation, and two for simulating rock types according to a given truncation rule. Furthermore, the dependence between copper grade and rock types is reproduced by considering cross correlations between these Gaussian random fields. To investigate the benefits of the joint simulation algorithm, copper grade and rock types are also simulated by the traditional cascade approach and the results are compared. It is shown that the cascade approach produces hard boundaries, that is, abrupt transitions of copper grades when crossing rock-type boundaries, a condition that does not exist in the study area according to the contact analysis held on the available data. In contrast, the joint simulation approach produces gradual transitions of the copper grade near the rock-type boundaries and is more suited to the actual data.CONICYT/FONDECYT/REGULAR/N◦113008