Convergency and Stability of Explicit and Implicit Schemes in the Simulation of the Heat Equation
| Autor: | Luis Rosales-Romero, Franyelit Suárez-Carreño |
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| Rok vydání: | 2021 |
| Předmět: |
Technology
Diffusion equation QH301-705.5 Differential equation QC1-999 020209 energy 02 engineering and technology 01 natural sciences Stability (probability) numerical methods 0202 electrical engineering electronic engineering information engineering Applied mathematics General Materials Science Polygon mesh Biology (General) 0101 mathematics QD1-999 Instrumentation Mathematics Fluid Flow and Transfer Processes diffusion equation Physics Process Chemistry and Technology Numerical analysis 010102 general mathematics General Engineering Finite difference method Engineering (General). Civil engineering (General) Computer Science Applications analytical solution Chemistry Distribution (mathematics) Heat equation TA1-2040 |
| Zdroj: | Applied Sciences, Vol 11, Iss 4468, p 4468 (2021) Applied Sciences Volume 11 Issue 10 |
| ISSN: | 2076-3417 |
| Popis: | Some strategies for solving differential equations based on the finite difference method are presented: forward time centered space (FTSC), backward time centered space (BTSC), and the Crank-Nicolson scheme (CN). These are developed and applied to a simple problem involving the one-dimensional (1D) (one spatial and one temporal dimension) heat equation in a thin bar. The numerical implementation in this work can be used as a preamble to introduce a method of solving the heat equation that can be implemented in problems in the area of finances. The results of implementing the software on very fine meshes (unidimensional), and with relatively small-time steps, are shown. Through mesh refinement, it was possible to obtain a better temperature distribution in the thin bar between a range of points. The heat equation was solved numerically by testing both implicit (CN) and explicit (FTSC and BTSC) methods. The examples show that the implemented schemes conform to theoretical predictions and that truncation errors depend on mesh, spacing, and time step. |
| Databáze: | OpenAIRE |
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