Usage of the finite difference method for solving one-dimensional heat equations ∗

Kirtiwant P Ghadle; Malayin A Mohammed; Aishwary K Ghadle

doi:10.48165/

Authors

Kirtiwant P Ghadle Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, Maharashtra-431 004, India.
Malayin A Mohammed Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, Maharashtra-431 004, India.
Aishwary K Ghadle Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, Maharashtra-431 004, India.

DOI:

https://doi.org/10.48165/

Keywords:

Finite difference method, One-dimensional heat equation, Uniqueness and stability

Abstract

In this paper the one-dimensional heat equations with the heat generation arising in the associated fractal transient conduction is investigated. Analytical solutions are obtained by using the finite difference method (FDM). The method, in general, is easy to implement and it yields good results. In addition, the uniqueness and stability results are also discussed. Some illustrative examples are included to demonstrate the validity and applicability of the technique.

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