51 research outputs found

    A collocation method based on discrete spline quasi-interpolatory operators for the solution of time fractional differential equations

    Get PDF
    In many applications, real phenomena are modeled by differential problems having a time fractional derivative that depends on the history of the unknown function. For the numerical solution of time fractional differential equations, we propose a new method that combines spline quasi-interpolatory operators and collocation methods. We show that the method is convergent and reproduces polynomials of suitable degree. The numerical tests demonstrate the validity and applicability of the proposed method when used to solve linear time fractional differential equations

    Isogeometric analysis of nonlinear eddy current problems

    Get PDF

    Construct Local Quasi-Interpolation Operators Using Linear B-Splines

    Get PDF
    The data interpolating problem is a fundamental problem in data analysis, and B-splines are frequently used as the basis functions for data interpolation. In the real-world applications, the real-time processing is very important. To achieve that, we cannot use any matrix inversion for large amount of data, and we also need to avoid using any global operator. To solve this problem, we develop a new method based on a local quasi-interpolation operator. To construct the local quasi-interpolation operator, we need to factorize the Shoenberg-Whitney matri- ces for the given data samples. Furthermore, our local quasi-interpolation operator should correspond to a band matrix with the minimum bandwidth, which is criti- cal for the real-time data processing. Finally, we bridge the gap between our local quasi-interpolation operator and a local spline interpolation operator through an impulse interpolation operator using a “blending” method

    On the numerical solution of fractional boundary value problems by a spline quasi-interpolant operator

    Get PDF
    Boundary value problems having fractional derivative in space are used in several fields, like biology, mechanical engineering, control theory, just to cite a few. In this paper we present a new numerical method for the solution of boundary value problems having Caputo derivative in space. We approximate the solution by the Schoenberg-Bernstein operator, which is a spline positive operator having shape-preserving properties. The unknown coefficients of the approximating operator are determined by a collocation method whose collocation matrices can be constructed efficiently by explicit formulas. The numerical experiments we conducted show that the proposed method is efficient and accurate

    Kontextsensitive Modellhierarchien für Quantifizierung der höherdimensionalen Unsicherheit

    Get PDF
    We formulate four novel context-aware algorithms based on model hierarchies aimed to enable an efficient quantification of uncertainty in complex, computationally expensive problems, such as fluid-structure interaction and plasma microinstability simulations. Our results show that our algorithms are more efficient than standard approaches and that they are able to cope with the challenges of quantifying uncertainty in higher-dimensional, complex problems.Wir formulieren vier kontextsensitive Algorithmen auf der Grundlage von Modellhierarchien um eine effiziente Quantifizierung der Unsicherheit bei komplexen, rechenintensiven Problemen zu ermöglichen, wie Fluid-Struktur-Wechselwirkungs- und Plasma-Mikroinstabilitätssimulationen. Unsere Ergebnisse zeigen, dass unsere Algorithmen effizienter als Standardansätze sind und die Herausforderungen der Quantifizierung der Unsicherheit in höherdimensionalen, komplexen Problemen bewältigen können
    • …
    corecore