High-order orthogonal spline collocation methods for two-point boundary value problems with interfaces

Santosh Kumar Bhal, P. Danumjaya and G. Fairweather

Mathematics and Computers in Simulation (MATCOM), 2020, vol. 174, issue C, 102-122

Abstract: Orthogonal spline collocation methods (OSC) are used to solve two-point boundary value problems (BVPs) with interfaces. We first consider the one-dimensional Helmholtz equation with piecewise wave numbers solved using the standard OSC approach. For the solution of self-adjoint two-point BVPs with interfaces, we employ OSC with monomial bases of degree r, where r=3,4. In each case, the results of numerical experiments involving numerous examples from the literature exhibit optimal accuracy in the L∞ and L2 norms of order r+1, and order r accuracy in the H1 norm. Moreover, superconvergence of order 2r−2 in the nodal error in the OSC approximation and also in its derivative when r=4 is observed. Each OSC approach gives rise to almost block diagonal linear systems which are solved using standard software.

Keywords: Two-point boundary value problems; Helmholtz equation; Interfaces; Orthogonal spline collocation methods; Monomial bases; Almost block diagonal linear systems; Optimal global error estimates; Superconvergence (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:174:y:2020:i:c:p:102-122

DOI: 10.1016/j.matcom.2020.03.001

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