Space-Time and Motion to Advection-Diffusion Equation
Abstract
We are concerned with the study the differential equation problem of space-time and motion for the case of advection-diffusion equation. We derive the advection-diffusion equation from the conservation of mass, where this can be represented by the substance flow in and flow out through the medium. In this case, the concentration of substance and rate of flow of substance in a medium are smooth functions which is useful to generate advection-diffusion equation. A special case of the advection-diffusion equation and numerical results are also given in this paper. We use explicit and implicit finite differences method for numerical results implemented in MATLAB.
Keywords: advection-diffusion; space-time; motion; finite difference method.
Abstrak
Kami tertarik untuk mempelajari masalah persamaan diferensial ruang-waktu, dan gerak untuk kasus persamaan adveksi-difusi. Kita menurunkan persamaan adveksi-difusi dari kekekalan massa, di mana hal ini dapat diwakili oleh aliran zat yang masuk dan keluar melalui media. Dalam hal ini konsentrasi zat dan laju aliran zat dalam suatu medium merupakan fungsi halus yang berguna untuk menghasilkan persamaan adveksi-difusi. Sebuah kasus khusus persamaan adveksi-difusi dan hasil numerik juga diberikan dalam makalah ini. Kami menggunakan metode beda hingga explisit dan implisit untuk hasil numerik yang diimplementasikan dalam MATLAB.
Kata kunci: adveksi-difusi; ruang-waktu; gerak; metode beda hingga.
Keywords
References
L. Debnath, Nonlinear Partial Differential Equations for Scientists and Engineering, Birkhauser, Boston, 1997.
Z. Erich, Partial Differential Equations of Applied Mathematics. Third Edition, Polytechnic University, New York: Wiley-Interscience, 2006.
G. Gurarslan, H. Karahan, D. Alkaya, M. Sari, M. Yasar, "Numerical Solution of Advection-Diffusion Equation Using a Sixth-Order Compact Finite Difference Method," Mathematical Problems in Engineering. 2013 (2013) 1–7.
Y. Hu, "Asymptotic nonlinear stability of traveling waves to a system of coupled Burgers equations," Journal of Mathematical Analysis and Applications. 397 (2013) 322-333.
P.M. Jordan, "A Note on the Lambert W-function: Applications in the matematical and physical sciences", Contemporary Mathematics, vol. 618, pp. 247-263, 2014.
R. Mickens and K. Oyedeji, "Traveling wave solutions to modified Burger's and diffusionless Fisher PDE's", Evolution Equations and Control Theory, vol. 8, pp. 139-147, 2019.
B. Pimpunchat, W.L. Sweatman, G.C. Wake, W. Triampo, and A. Parshotan, "A mathematical model for pollution in a river and its remediation by aeration," Applied Mathematical Letter, vol. 22, pp. 304, 2009.
G.B. Whitham, Linear and Nonlinear waves, Wiley-Interscience, New York, 1974.
DOI: 10.15408/inprime.v3i1.19679
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