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偏微分方程導論
八十九學年度第二學期

ㄧ些常見的PDE例子

One-Dimensional Hyperbolic Equations

(I) Initial Value Problems

Example 1: Linear advection equation ( 方程式描述 ), ( 動畫 ), ( Space-Time plot ), ( Matlab M-file).
Example 2: Inviscid Burger's equation ( 方程式描述 ), ( 動畫 ), ( Matlab M-file).
Example 3: Wave equation ( 方程式描述 ), ( 動畫1 ), ( 動畫2 ), ( Matlab M-file).

(II) Initial-Boundary Value Problems

Example 1: Wave equation ( Space-Time plot ), ( Matlab M-file).

One-Dimensional Parabolic Equations

(I) Initial Value Problems

Example 1: Linear heat equation ( 方程式描述 ), ( 動畫 ), ( Matlab M-file).
Example 2: Burger's equation ( 方程式描述 ).

(II) Initial-Boundary Value Problems

Example 1: Black-Scholes equation ( 方程式描述 ), ( Space-Time Plot ), ( Matlab M-file).

Two-Dimensional Elliptic equations

Example 1: Laplace's equation ( 方程式描述 ),
Example 2: Poisson's equation ( 方程式描述 ).

Two-Dimensional Hyperbolic Equations

Two-Dimensional Parabolic Equations

Schroedinger Equation

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