108
个编辑
更改
跳到导航
跳到搜索
第712行：
第712行： − +
→Analytical solutions
If and are solutions of linear PDE in some function space , then c<sub>1</sub>u<sub>1</sub> + c<sub>2</sub>u<sub>2</sub>}} with any constants and are also a solution of that PDE in the same function space.
If and are solutions of linear PDE in some function space , then c<sub>1</sub>u<sub>1</sub> + c<sub>2</sub>u<sub>2</sub>}} with any constants and are also a solution of that PDE in the same function space.
若线性偏微分方程在某个函数空间{{mvar|R}}中有解{{math|''u''<sub>1</sub>}} 和 {{math|''u''<sub>2</sub>}}，则{{math|''u'' {{=}} ''c''<sub>1</sub>''u''<sub>1</sub> + ''c''<sub>2</sub>''u''<sub>2</sub>}，其中{{math|''c''<sub>1</sub>}} 和 {{math|''c''<sub>2</sub>}}是任意常数，也是该偏微分方程在同一函数空间中的解。
若线性偏微分方程在某个函数空间{{mvar|R}}中有解{{math|''u''<sub>1</sub>}} 和 {{math|''u''<sub>2</sub>}}，则{{math|''u'' {{=}} ''c''<sub>1</sub>''u''<sub>1</sub> + ''c''<sub>2</sub>''u''<sub>2</sub>}，也是该偏微分方程在同一函数空间中的解，其中{{math|''c''<sub>1</sub>}} 和 {{math|''c''<sub>2</sub>}} 是任意常数。
===Methods for non-linear equations===
===Methods for non-linear equations===