Abstract
This study aims at constructing new and effective fully explicit numerical schemes for solving the heat conduction equation. We use fractional time steps for the odd cells in the well-known odd–even hopscotch structure and fill it with several different formulas to obtain a large number of algorithm combinations. We generate random parameters in a highly inhomogeneous spatial distribution to set up discretized systems with various stiffness ratios, and systematically test these new methods by solving these systems. The best combinations are verified by comparing them to analytical solutions. We also show analytically that their rate of convergence is two and that they are unconditionally stable.
Supplementary Materials
The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/IOCA2021-10902/s1.
Funding
The research was funded by the ÚNKP-21-3 new national excellence program of the ministry for innovation and technology from the source of the national research, development and innovation fund.
Informed Consent Statement
Informed consent was obtained from all subjects involved in the study.
Data Availability Statement
No data is available.
Conflicts of Interest
The authors declare no conflict of interest.
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