Pairtial differential equation

In mathematics, a pairtial differential equation (PDE) is a differential equation that contains unkent multivariable functions an thair pairtial derivatives. (A special case are ordinary differential equations (ODEs), which deal wi functions o a single variable an thair derivatives.)

A visualisation o a solution to the heat equation on a three dimensional plane

Relatit page: Numerical methods for pairtial differential equations

References

• Partial Differential Equations (Graduate Studies in Mathematics) Lawrence C. Evans, American Mathematical Society.
• Partial Differential Equations I-III (Applied Mathematical Sciences) Michael Taylor, Springer.
• Egorov, Y. V., & Shubin, M. A. (2013). Foundations of the classical theory of partial differential equations. Springer Science & Business Media.
• Egorov, Komech and Shubin - Elements of the Modern Theory of Partial Differential Equations (1999) Springer.
• Sommerfeld, A. (1949). Partial differential equations in physics. Academic Press.
• Renardy, M., & Rogers, R. C. (2006). An introduction to partial differential equations. Springer Science & Business Media.
• Olver, P. J., Introduction to partial differential equations. Berlin: Springer.

Further Readin

• 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.
• M. Nakao, M. Plum, Y. Watanabe (2019) Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations (Springer Series in Computational Mathematics).

Researchers

• Leonid Kantorovich
• Ryogo Hirota
• Sofia Kovalevskaya