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BS2 methods for semi-linear second order boundary value problems

Author

Listed:
  • Manni, Carla
  • Mazzia, Francesca
  • Sestini, Alessandra
  • Speleers, Hendrik

Abstract

A new class of Linear Multistep Methods based on B-splines for the numerical solution of semi-linear second order Boundary Value Problems is introduced. The presented schemes are called BS2 methods, because they are connected to the BS (B-spline) methods previously introduced in the literature to deal with first order problems. We show that, when using an even number of steps, schemes with good general behavior are obtained. In particular, the absolute stability of the 2-step and 4-step BS2 methods is shown. Like BS methods, BS2 methods are of particular interest, because it is possible to associate with the discrete solution a spline extension which collocates the differential equation at the mesh points.

Suggested Citation

  • Manni, Carla & Mazzia, Francesca & Sestini, Alessandra & Speleers, Hendrik, 2015. "BS2 methods for semi-linear second order boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 147-156.
    • Handle: RePEc:eee:apmaco:v:255:y:2015:i:c:p:147-156
    DOI: 10.1016/j.amc.2014.08.046
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    Cited by:

    1. Ramos, Higinio & Singh, Gurjinder, 2022. "Solving second order two-point boundary value problems accurately by a third derivative hybrid block integrator," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    2. Costabile, Francesco A. & Gualtieri, Maria Italia & Serafini, Giada, 2017. "Cubic Lidstone-Spline for numerical solution of BVPs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 56-64.
    3. Ramos, Higinio & Rufai, M.A., 2019. "A third-derivative two-step block Falkner-type method for solving general second-order boundary-value systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 139-155.
    4. Zhao, Jingjun & Jiang, Xingzhou & Xu, Yang, 2022. "Fully discretized methods based on boundary value methods for solving diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 418(C).

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