Efficient 1D Heat Equation Solver: Leveraging Numba in Python

Sandy Hardian Susanto Herho; Siti Nurzannah  Kaban; Dasapta Erwin Irawan; Rubiyanto Kapid

doi:10.24036/eksakta/vol25-iss02/487

EKSAKTA: Berkala Ilmiah Bidang MIPA

Open Access

Efficient 1D Heat Equation Solver: Leveraging Numba in Python

Sandy Hardian Susanto Herho ¹

, Siti Nurzannah Kaban ²

, Dasapta Erwin Irawan ³

, Rubiyanto Kapid ⁴

¹ Department of Earth and Planetary Sciences, University of California, Riverside, USA

² School of Architecture, Planning and Perservation, University of Maryland, College Park, MD, USA

³ Applied Geology Research Group, Bandung Institute of Technology, Bandung, Indonesia

⁴ Paleontology and Quaternary Geology Research Group, Bandung Institute of Technology, Bandung, Indonesia

Published 2024-06-30

Vol. 25 No. 02 (2024) PAGES 126-137

DOI 10.24036/eksakta/vol25-iss02/487

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Abstract

This paper presents a Numba-based solver for the 1D Heat Equation, seamlessly blending Pythonâ€™s readability with Numbaâ€™s dynamic Just-In-Time (JIT) compilation. The explicit method exhibits a notable runtime reduction from 8.324 s to 4.035 s, while the implicit method sees a more pronounced improvement, decreasing from 9.970 s to 1.195 s. Statistical tests confirm the statistical significance of these efficiency gains. Future research directions include extending the solver to multidimensional heat equations, exploring advanced parallelization techniques, and implementing dynamic parameter optimization strategies. Collaboration with domain experts for real-world applications is also envisioned to validate the solverâ€™s performance and impact. In summary, the symbiosis of Python and Numba in crafting an optimized 1D Heat Equation solver marks a pivotal advancement in efficient numerical solutions. This research holds promise for diverse scientific

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Efficient 1D Heat Equation Solver: Leveraging Numba in Python

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Efficient 1D Heat Equation Solver: Leveraging Numba in Python

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