Solving Differential and Integro-Differential Boundary Value Problems using a Numerical Sinc-Collocation Method Based on Derivative Interpolation

Abstract

In this thesis, a new sinc-collocation method based upon derivative interpolation is developed for solving linear and nonlinear boundary value problems involving differential as well as integro-differential equations. The sinc-collocation method is chosen for its ease of implementation, exponential convergence of error, and ability to handle to singularities in the BVP. We present a unique method of treating boundary conditions and introduce the concept of the stretch factor into the conformal mappings of domains. The result is a method that achieves great accuracy while reducing computational cost. In most cases, the results from the method greatly exceed the published results of comparable methods in both accuracy and efficiency. The method is tested on the Blasius problem, the Lane-Emden problem and generalised to cover Fredholm-Volterra integro-differential problems. The results show that the sinc-collocation method with derivative interpolation is a viable and preferable method for solving nonlinear BVPs.

Author Keywords: Blasius, Boundary Value Problem, Exponential convergence, Integro-differential, Nonlinear, Sinc

    Item Description
    Type
    Contributors
    Creator (cre): Ross, Glen Charles
    Thesis advisor (ths): Abdella, Kenzu
    Degree committee member (dgc): Pollanen, Marco
    Degree granting institution (dgg): Trent University
    Date Issued
    2020
    Date (Unspecified)
    2020
    Place Published
    Peterborough, ON
    Language
    Extent
    167 pages
    Rights
    Copyright is held by the author, with all rights reserved, unless otherwise noted.
    Local Identifier
    TC-OPET-10772
    Publisher
    Trent University
    Degree