Exploring the advection-diffusion equation through the subdivision collocation method: a numerical study

被引：0
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作者：
Safia Malik
Syeda Tehmina Ejaz
Ali Akgül
Murad Khan Hassani
机构：
[1] The Government Sadiq College Women University Bahawalpur,Department of Mathematics
[2] Lebanese American University,Department of Computer Science and Mathematics
[3] Siirt University,Art and Science Faculty, Department of Mathematics
[4] Near East University,Mathematics Research Center, Department of Mathematics
[5] Ghazni University,Department of Mathematics
来源：
Scientific Reports | / 14卷
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摘要：
The current research presents a novel technique for numerically solving the one-dimensional advection-diffusion equation. This approach utilizes subdivision scheme based collocation method to interpolate the space dimension along with the finite difference method for the time derivative. The proposed technique is examined on a variety of problems and the obtained results are presented both quantitatively in tables and visually in figures. Additionally, a comparative analysis is conducted between the numerical outcomes of the proposed technique with previously published methods to validate the correctness and accuracy of the current approach. The primary objective of this research is to investigate the application of subdivision schemes in the fields of physical sciences and engineering. Our approach involves transforming the problem into a set of algebraic equations.
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