Integrasi Romberg dan Monte Carlo, Dua Pendekatan Berbeda Untuk Solusi Sistem Reverse Osmosis Pada Media Berpori

Hery Andi Sitompul; Dewi Sholeha

doi:10.59086/jti.v4i3.1339

Authors

Hery Andi Sitompul Universitas HKBP Nommensen, Medan
Dewi Sholeha Universitas Darma Agung, Medan

DOI:

https://doi.org/10.59086/jti.v4i3.1339

Abstract

Sistem reverse osmosis merupakan metode yang sangat populer untuk pemurnian air dengan memanfaatkan aliran air dari pori – pori media yang semi permeabel. Pemodelan matematis untuk sistem ini dilakukan dengan pendekatan persamaan adveksi-difusi berbentuk persamaan diferensial parsial. Dalam persamaan solusi eksak sistem reverse osmosis pada penelitian sebelumnya terdapat bentuk integral tak wajar, dimana integral secara analitik sulit dilakukan. Integrasi secara numerik merupakan pilihahan satu-satunya untuk menyelesaikan integral tersebut. Dalam kajian ini Pendekatan numerik secara deterministik dan stokastik dilakukan untuk menyelesaikan bentuk integral tersebut. Integrasi Romberg orde-10 menghasilkan solusi yang paling optimum untuk solusi persamaan adveksi-difusi pada sistem reverse osmosis.

The reverse osmosis system is a very popular method for water purification by utilizing water flow from the pores of a semi-permeable medium. Mathematical modeling for this system is carried out using an advection-diffusion equation approach in the form of a partial differential equation. In the exact solution equation of the reverse osmosis system in previous studies, there is an improper integral form, where integration is analytically difficult to perform. Numerical integration is the only option for solving this integral. In this study, deterministic and stochastic numerical approaches are used to solve this integral form. The 10th order Romberg integration produces the most optimal solution for the advection-diffusion equation in the reverse osmosis system.

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