Testing and comparing the performance of numerical methods for the heat conduction equation partial differential equation
This research collected 12 numerical algorithms that solve the transient diffusion equation with Dirichlet boundary conditions in one space dimension. Some of these methods are explicit and unconditionally stable simultaneously. A nontrivial analytical solution, recently obtained by a self-similar A...
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| Published in | Multidiszciplinaris Tudomanyok Vol. 15; no. 1; pp. 79 - 88 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
09.07.2025
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| Online Access | Get full text |
| ISSN | 2062-9737 2786-1465 2786-1465 |
| DOI | 10.35925/j.multi.2025.1.7 |
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| Abstract | This research collected 12 numerical algorithms that solve the transient diffusion equation with Dirichlet boundary conditions in one space dimension. Some of these methods are explicit and unconditionally stable simultaneously. A nontrivial analytical solution, recently obtained by a self-similar Ansatz, served as the reference solution. The errors were calculated and plotted as a function of the time step size and execution times. The conclusion is that there are explicit and stable methods that provide acceptable results faster than the traditional Runge-Kutta style methods. |
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| AbstractList | This research collected 12 numerical algorithms that solve the transient diffusion equation with Dirichlet boundary conditions in one space dimension. Some of these methods are explicit and unconditionally stable simultaneously. A nontrivial analytical solution, recently obtained by a self-similar Ansatz, served as the reference solution. The errors were calculated and plotted as a function of the time step size and execution times. The conclusion is that there are explicit and stable methods that provide acceptable results faster than the traditional Runge-Kutta style methods. |
| Author | Hriczó, Krisztián Barna, Imre Ferenc Zain, Andicha |
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| Snippet | This research collected 12 numerical algorithms that solve the transient diffusion equation with Dirichlet boundary conditions in one space dimension. Some of... |
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| Title | Testing and comparing the performance of numerical methods for the heat conduction equation partial differential equation |
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