A Novel Space-Time Marching Method for Solving Linear and Nonlinear Transient Problems
Abstract
:1. Introduction
2. Numerical Method
2.1. Marching Method
2.1.1. Time Marching Method
2.1.2. Space-Time Method
2.1.3. Space-Time Marching Method
2.2. Space-Time Polyharmonic Radial Polynomial Basis Functions
2.3. Fictitious Time Integration Method
3. Validation
4. Numerical Example
4.1. Diffusion Equation with Sources and Sinks
4.2. Convection–Diffusion Equation
4.3. Burgers–Fisher Equation
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
PDEs | partial differential equations |
FDM | finite difference method |
RBFCM | radial basis function collocation method |
ST | space-time |
FTIM | fictitious time integration method |
MQ | multiquadrics |
IMQ | inverse multiquadrics |
PS | polyharmonic spline |
RPBFs | radial polynomial basis functions |
MAE | max absolute error |
RMSE | root mean square error |
MLRPI | meshless local radial point interpolation |
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Hong, L.-D.; Ku, C.-Y.; Liu, C.-Y. A Novel Space-Time Marching Method for Solving Linear and Nonlinear Transient Problems. Mathematics 2022, 10, 4694. https://doi.org/10.3390/math10244694
Hong L-D, Ku C-Y, Liu C-Y. A Novel Space-Time Marching Method for Solving Linear and Nonlinear Transient Problems. Mathematics. 2022; 10(24):4694. https://doi.org/10.3390/math10244694
Chicago/Turabian StyleHong, Li-Dan, Cheng-Yu Ku, and Chih-Yu Liu. 2022. "A Novel Space-Time Marching Method for Solving Linear and Nonlinear Transient Problems" Mathematics 10, no. 24: 4694. https://doi.org/10.3390/math10244694
APA StyleHong, L.-D., Ku, C.-Y., & Liu, C.-Y. (2022). A Novel Space-Time Marching Method for Solving Linear and Nonlinear Transient Problems. Mathematics, 10(24), 4694. https://doi.org/10.3390/math10244694