This paper studies an alternating direction implicit orthogonal spline collocation (ADIOSC) technique for calculating the numerical solution of hyperbolic integrodifferential problem with a weakly singular kernel in two-dimensional domain. The integral term is approximated help second-order fractional quadrature formula introduced by Lubich. stability and convergence analysis proposed strategy ...

This study presents the results of a microwave-based algorithm which attempts to perform the retrieval of hydrometeor parameters in a profile form. The hydrometeors in question are both phases of the precipitating rain (liquid and frozen). The algorithm is called the Microwave Integrated Retrieval System (MiRS) which uses microwave radiances from AMSU and MHS sensors onboard NOAA-18, NOAA-19, M...

Nonintrusive polynomial chaos expansion (PCE) and stochastic collocation (SC) methods are attractive techniques for uncertainty quantification due to their fast convergence properties and ability to produce functional representations of stochastic variability. PCE estimates coefficients for known orthogonal polynomial basis functions based on a set of response function evaluations, using sampli...

An accurate and efficient solution method using spectral collocation method with domain decomposition is proposed for computing optical waveguides with discontinuous refractive index profiles. The use of domain decomposition divides the usual single domain into a few subdomains at the interfaces of discontinuous refractive index profiles. Each subdomain can be expanded by a suitable set of orth...

Abstract. A local convergence rate is established for a Gauss orthogonal collocation method applied to optimal control problems with control constraints. If the Hamiltonian possesses a strong convexity property, then the theory yields convergence for problems whose optimal state and costate possess two square integrable derivatives. The convergence theory is based on a stability result for the ...

In this paper, a Jacobi-collocation spectral method is developed for Volterra integral equations of second kind with a weakly singular kernel. We use some function transformation and variable transformations to change the equation into a new Volterra integral equation defined on the standard interval [−1, 1], so that the solution of the new equation possesses better regularity and the Jacobi or...

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equi...

Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It one most general methods when compared to other techniques. PDEs posed in a variational form over given space, say Hilbert are better numerically handled with FEM. The FEM algorithm used various applications which includes fluid flow, heat transfer, acoustics, structural mech...