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All Journal JTAM (Jurnal Teori dan Aplikasi Matematika) Journal of Science and Technology
Syafi'i, Mohamad
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Computer Science & IT Mathematics

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Journal : JTAM (Jurnal Teori dan Aplikasi Matematika)

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Numerical Solution of the Advection-Diffusion Equation Using the Radial Basis Function Sabran, La Ode; Syafi'i, Mohamad
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 4 (2023): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i4.16239

Abstract

The advection-diffusion equation is a form of partial differential equation. This equation is also known as the transport equation. The purpose of this research is to approximatio the solution of advection-diffusion equation  by numerical approach using radial basis functions network. The approximation is performed by using the multiquadrics basis function. The simulation of the numerical solution is run with the help of the Matlab program. The one-dimensional advection-diffusion equation used is  ∂u/∂t+C ∂u/∂x=D (∂^2 u)/(∂x^2 )  with given initial conditions, boundary conditions, and exact solution u(x,t). The numerical solution approximation using the radial basis function network with dt=0.004 and dx=0.02 produces the value at each discretization point is close to the exact solution. In this study, the smallest error between numerical solution and the exact solution is obtained 2.18339 ×〖10〗^(-10).
Co-Authors Miftahul Jannah Sabran, La Ode Yulia, Rahma