Numerical methods for pairtial differential equations

Numerical methods for partial differential equations are computational schemes tae obtain approximate solutions o pairtial differential equations (PDEs).

Journal

The scientific journal "numerical methods for partial differential equations" is publishit tae promote the studies o this area^[1].

Relatit saftware

Chebfun is ane o the most famous saftware i this field^[2]^[3]^[4]^[5]. They are also many libraries such as:

FreeFem++^[6]^[7]^[8]
FEniCS Project^[9]^[10]^[11]^[12]

References

↑ Numerical Methods for Partial Differential Equations, Wiley Online Library
↑ Driscoll, T. A., Hale, N., & Trefethen, L. N. (2014). Chebfun guide.
↑ Platte, R. B., & Trefethen, L. N. (2010). Chebfun: a new kind of numerical computing. In Progress in industrial mathematics at ECMI 2008 (pp. 69-87). Springer, Berlin, Heidelberg.
↑ Hashemi, B., & Trefethen, L. N. (2017). Chebfun in three dimensions. SIAM Journal on Scientific Computing, 39(5), C341-C363.
↑ Wright, G. B., Javed, M., Montanelli, H., & Trefethen, L. N. (2015). Extension of Chebfun to periodic functions. SIAM Journal on Scientific Computing, 37(5), C554-C573.
↑ Hecht, F. (2012). New development in FreeFem++. Journal of numerical mathematics, 20(3-4), 251-266.
↑ Hecht, F., Pironneau, O., Le Hyaric, A., & Ohtsuka, K. (2005). FreeFem++ manual.
↑ Sadaka, G. (2012). FreeFem++, a tool to solve PDEs numerically. arXiv preprint arXiv:1205.1293.
↑ Alnæs, M., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., ... & Wells, G. N. (2015). The FEniCS project version 1.5. Archive of Numerical Software, 3(100).
↑ Dupont, T., Hoffman, J., Johnson, C., Kirby, R. C., Larson, M. G., Logg, A., & Scott, L. R. (2003). The fenics project. Chalmers Finite Element Centre, Chalmers University of Technology.
↑ Logg, A., Mardal, K. A., & Wells, G. (Eds.). (2012). Automated solution of differential equations by the finite element method: The FEniCS book. en:Springer Science & Business Media.
↑ Langtangen, H. P., Logg, A., & Tveito, A. (2016). Solving PDEs in Python: The FEniCS Tutorial I. Springer International Publishing.

Further Readin

Iserles, A. (2009). A first course in the numerical analysis of differential equations. Cambridge University Press.
Computational Partial Differential Equations Using MATLAB, Jichun Li and Yi-Tung Chen, Chapman & Hall.
Ames, W. F. (2014). Numerical methods for partial differential equations. Academic Press.
Ganzha, V. G. E., & Vorozhtsov, E. V. (1996). Numerical solutions for partial differential equations: problem solving using Mathematica. CRC Press.

Experts

External links

Numerical Methods for Partial Differential Equations course.
IMS, the Open Source IMTEK Mathematica Supplement (IMS)
Numerical PDE Techniques for Scientists and Engineers

[1] Numerical Methods for Partial Differential Equations, Wiley Online Library

[2] Driscoll, T. A., Hale, N., & Trefethen, L. N. (2014). Chebfun guide.

[3] Platte, R. B., & Trefethen, L. N. (2010). Chebfun: a new kind of numerical computing. In Progress in industrial mathematics at ECMI 2008 (pp. 69-87). Springer, Berlin, Heidelberg.

[4] Hashemi, B., & Trefethen, L. N. (2017). Chebfun in three dimensions. SIAM Journal on Scientific Computing, 39(5), C341-C363.

[5] Wright, G. B., Javed, M., Montanelli, H., & Trefethen, L. N. (2015). Extension of Chebfun to periodic functions. SIAM Journal on Scientific Computing, 37(5), C554-C573.

[6] Hecht, F. (2012). New development in FreeFem++. Journal of numerical mathematics, 20(3-4), 251-266.

[7] Hecht, F., Pironneau, O., Le Hyaric, A., & Ohtsuka, K. (2005). FreeFem++ manual.

[8] Sadaka, G. (2012). FreeFem++, a tool to solve PDEs numerically. arXiv preprint arXiv:1205.1293.

[9] Alnæs, M., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., ... & Wells, G. N. (2015). The FEniCS project version 1.5. Archive of Numerical Software, 3(100).

[10] Dupont, T., Hoffman, J., Johnson, C., Kirby, R. C., Larson, M. G., Logg, A., & Scott, L. R. (2003). The fenics project. Chalmers Finite Element Centre, Chalmers University of Technology.

[11] Logg, A., Mardal, K. A., & Wells, G. (Eds.). (2012). Automated solution of differential equations by the finite element method: The FEniCS book. en:Springer Science & Business Media.

[12] Langtangen, H. P., Logg, A., & Tveito, A. (2016). Solving PDEs in Python: The FEniCS Tutorial I. Springer International Publishing.

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