Partial differential equation

differential equation that contains unknown multivariable functions and their partial derivatives

Partial differential equations (abbreviated as PDEs) are a kind of mathematical equation. They are related to partial derivatives, in that obtaining an antiderivative of a partial derivative involves integration of partial differential equations.

Numerical methods


Since PDEs have appeared in mathematics and physics, many scientists have studied methods to solve them. But unfortunately, no one could establish methods to solve any kind of PDE. Therefore, numerical methods for PDEs (such as the finite element method) are widely studied since the appearance of computers.[1][2][3]


People who studied about partial differential equations



  • Partial Differential Equations (Graduate Studies in Mathematics) Lawrence C. Evans, American Mathematical Society, 2010/04/.
  • Egorov, Y. V., & Shubin, M. A. (2013). Foundations of the classical theory of partial differential equations. Springer Science & Business Media.
  • Olver, P. J., Introduction to partial differential equations. Berlin: Springer.
  • Partial Differential Equations I-III (Applied Mathematical Sciences) Michael Taylor, Springer.


  1. Iserles, A. (2009). A first course in the numerical analysis of differential equations. Cambridge University Press.
  2. Ames, W. F. (2014). Numerical methods for partial differential equations. Academic Press.
  3. M. Nakao, M. Plum, Y. Watanabe (2019) Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations (Springer Series in Computational Mathematics).