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Numerical methods for pairtial differential equations

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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:

References

  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.

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.

See also

Experts

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