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Using an Integrating Factor to Transform a Second Order BVP to a Fixed Point Problem

In: Mathematical Analysis in Interdisciplinary Research

Author

Listed:
  • Richard I. Avery

    (Dakota State University)

  • Douglas R. Anderson

    (Concordia College)

  • Johnny Henderson

    (Baylor University)

Abstract

Using an integrating factor, a second order boundary value problem is transformed into a fixed point problem. We provide growth conditions for the existence of a fixed point to the associated operator for this transformation and conclude that the index of the operator applying the standard Green’s function approach is zero; this does not guarantee the existence of a solution, demonstrating the value and potential for this new transformation.

Suggested Citation

  • Richard I. Avery & Douglas R. Anderson & Johnny Henderson, 2021. "Using an Integrating Factor to Transform a Second Order BVP to a Fixed Point Problem," Springer Optimization and Its Applications, in: Ioannis N. Parasidis & Efthimios Providas & Themistocles M. Rassias (ed.), Mathematical Analysis in Interdisciplinary Research, pages 101-108, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-84721-0_7
    DOI: 10.1007/978-3-030-84721-0_7
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