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PDE Review

PDE Review

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PDE Review For S.-T. Yau College Student Mathematics Contests

Laplace Equation

Harmonic Function

Mean value formula Harnack Thm;Liouville Thm.

Fundamental solution

Green Function

Energy

Separation of variables

Five point finite scheme

It is so easy,Error analysis:
$||e_h||=||U-u||\le K||L_hU-L_hu||\le K(||LhU-\hat L u||+||\hat Lu-Lhu||)$

Heat Equation

Fourier Methods

Wave Equation

Characteristic Method

Energy

Conservation law

Dispersive and Dissipative

Finite Difference Scheme

Lax Equivlance Thm

Thm.对于一个给定的适定的线性发展方程,定义一个一致可解的相容的线性差分格式,格式的稳定性是其收敛的充分必要条件。

Modified equation