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On the Existence, Uniqueness and Application of the Finite Difference Method for Solving Robin Elliptic Boundary Value Problem

Author

Listed:
  • Germain Nguimbi
  • Diogene Vianney Pongui Ngoma
  • Vital Delmas Mabonzo
  • Bienaime Bervi Bamvi Madzou
  • Melchior Josièrne Jupy Kokolo

Abstract

This paper refers to mathematical modelling and numerical analysis. The analysis to be presented through this paper deals with Robin’s problem which boundary equation is a linear combination of Dirichlet and Neumann-type boundary condi-tions. For this purpose we proved the existence and uniqueness of the solution. It is worth noting that the implementation of numerical simulations depends on the type of problem since it requires a search for explicit solution. Consequently, the motivation exists in this paper for choosing a classical method of variation of constants and employing a finite difference method to find the exact and numerical solutions, respectively so that numerical simulations were implemented in Scilab.

Suggested Citation

  • Germain Nguimbi & Diogene Vianney Pongui Ngoma & Vital Delmas Mabonzo & Bienaime Bervi Bamvi Madzou & Melchior Josièrne Jupy Kokolo, 2019. "On the Existence, Uniqueness and Application of the Finite Difference Method for Solving Robin Elliptic Boundary Value Problem," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(1), pages 26-36, February.
    • Handle: RePEc:ibn:jmrjnl:v:11:y:2019:i:1:p:26
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    More about this item

    Keywords

    Robin problem; finite difference method; numerical simulations;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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