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

Author

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  • Bhal, Santosh Kumar
  • Danumjaya, P.
  • Fairweather, G.

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.

Suggested Citation

  • Bhal, Santosh Kumar & Danumjaya, P. & Fairweather, G., 2020. "High-order orthogonal spline collocation methods for two-point boundary value problems with interfaces," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 102-122.
    • Handle: RePEc:eee:matcom:v:174:y:2020:i:c:p:102-122
    DOI: 10.1016/j.matcom.2020.03.001
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