Eksplorasi hubungan persamaan gelombang satu dimensi dengan random walks problems, ekspektasi, varians, dan unidirectional linear wave motion
Abstract
Understanding partial differential equations (PDEs) is crucial in the realm of science. PDEs involve two or more independent variables and can be applied across various fields. One widely used PDE is the one-dimensional wave equation, which represents everyday physical phenomena. This research explores the relationship between the one-dimensional wave equation and several related topics, such as random walks problems, expectation and variance, and unidirectional linear wave motion. First, the study discusses the fundamentals of the one-dimensional wave equation and its solution methods. Next, it examines the correlation between the wave equation and random walks problems, providing insights into the movement of particles or waves within a specific medium. The analysis then delves into the expectation and variance of temperature in a statistical context to understand the energy distribution or complex wave phenomena. Finally, the research investigates unidirectional linear wave motion and its application in solving problems using the method of characteristics.
Downloads
References
Khamidiyah, K., & Pagalay, U. (2014). Diskritisasi pada sistem persamaan diferensial parsial pola pembentukan sel. 3(3).
Levine, H. (1978). Unidirectional wave motions. North-Holland Pub. Co.
Maulidi, I. (2018). Metode beda hingga untuk penyelesaian persamaan diferensial parsial. https://doi.org/10.31219/osf.io/q526f
Noor, A. A., Putri, A. R., & Syafwan, M. (2019). Solusi analitik dan numerik suatu persamaan gelombang satu dimensi. Jurnal Matematika UNAND, 8(4), 1. https://doi.org/10.25077/jmu.8.4.1-8.2019
Xia, F., Liu, J., Nie, H., Fu, Y., Wan, L., & Kong, X. (2020). Random walks: a review of algorithms and applications. IEEE Transactions on Emerging Topics in Computational Intelligence, 4(2), 95–107. https://doi.org/10.1109/TETCI.2019.2952908
Copyright (c) 2024 Siti Safira Khoirotunnisa
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work’s authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal’s published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
