微分方程数值解法实验报告4

一维抛物方程的初边值问题

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微分方程数值解法实验报告

一维抛物方程的初边值问题

数值求解流程(图): 输入时间步长、空间步长、网格数，给边界条件赋值，利用式(3.1)经过多次迭代，进行 计算。利用 Matlab 计算，在窗口命令中输入 fwave(10,0.1,10,0.05,0,2),便可得到在该条件下的结果。

采用 Matlab 程序设计语言编程实现该问题的数值求解。 在 Matlab 命令窗口中输入命令：T=0.5 时：fwave(10,0.1,10,0.05,0,2) T=1.5 时：fwave(10,0.1,30,0.05,0,2) T=1.0 时：fwave(10,0.1,20,0.05,0,2) T=2.0 时：fwave(10,0.1,40,0.05,0,2)

运行程序得到实验结果为： T=0.5 时：fwave(10,0.1,10,0.05,0,2) ans = Columns 1 through 5 0 1.9021 0 1.9021 0 1.7159 0 1.3618 0 0.8743 0 0.3013 0 -0.3013 0 -0.8743 0 -1.3618 0 -0.5575 -1.0605 -1.4596 -0.4425 -0.8416 -1.1584 -1.3618 0 -0.5575 -1.0605 -1.4596 -0.2841 -0.5404 -0.7437 -0.8743 0 -0.4425 -0.8416 -1.1584 -0.0979 -0.1862 -0.2563 -0.3013 0 -0.2841 -0.5404 -0.7437 0.0979 0.1862 0.2563 0.3013 0 -0.0979 -0.1862 -0.2563 0.2841 0.5404 0.7437 0.8743 0 0.0979 0.1862 0.2563 0.4425 0.8416 1.1584 1.3618 0 0.2841 0.5404 0.7437 0.5575 1.0605 1.4596 1.7159 0 0.4425 0.8416 1.1584 0.6180 1.1756 1.6180 1.9021 0 0.5575 1.0605 1.4596 0.6180 1.1756 1.6180 1.9021 0 0.6180 1.1756 1.6180

T=1.0 时：fwave(10,0.1,20,0.05,0,2) ans = Columns 1 through 5 0 0.6180 1.1756 1.6180

一维抛物方程的初边值问题

-1.7159 0 -1.9021 Columns 6 through 10 2.0000 0.6180 2.0000 0.6180 1.8042 0.5575 1.4318 0.4425 0.9193 0.2841 0.3168 0.0979 -0.3168 -0.0979 -0.9193 -0.2841 -1.4318 -0.4425 -1.8042 -0.5575 -2.0000 -0.6180 Column 11 0.0000 0.0000 -0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0 0 1.9021 1.9021 1.7159 1.3618 0.8743 0.3013 -0.3013 -0.8743 -1.3618 -1.7159 -1.9021 1.6180 1.6180 1.4596 1.1584 0.7437 0.2563 -0.2563 -0.7437 -1.1584 -1.4596 -1.6180 1.1756 1.1756 1.0605 0.8416 0.5404 0.1862 -0.1862 -0.5404 -0.8

416 -1.0605 -1.1756 -0.6180 -1.1756 -1.6180

-1.7159 0 -1.9021 0 -1.9021 0 -1.7159 0 -1.3618 0 -0.8743 0 -0.3013 0 0.3013 0 0.8743 0 1.3618 0 1.7159 0 1.9021 Columns 6 through 10 2.0000 0.6180 2.0000 0.6180 1.8042 0.5575 1.4318 0.4425 0.9193 0.2841 0.3168 0.0979 -0.3168 -0.0979 -0.9193 -0.2841 -1.4318 -0.4425 1.9021 1.9021 1.7159 1.3618 0.8743 0.3013 -0.3013 -0.8743 -1.3618 1.6180 1.6180 1.4596 1.1584 0.7437 0.2563 -0.2563 -0.7437 -1.1584 1.1756 1.1756 1.0605 0.8416 0.5404 0.1862 -0.1862 -0.5404 -0.8416 0.6180 1.1756 1.6180 0.5575 1.0605 1.4596 0.4425 0.8416 1.1584 0.2841 0.5404 0.7437 0.0979 0.1862 0.2563 -0.0979 -0.1862 -0.2563 -0.2841 -0.5404 -0.7437 -0.4425 -0.8416 -1.1584 -0.5575 -1.0605 -1.4596 -0.6180 -1.1756 -1.6180 -0.6180 -1.1756 -1.6180

一维抛物方程的初边值问题

-1.8042 -0.5575 -2.0000 -0.6180 -2.0000 -0.6180 -1.8042 -0.5575 -1.4318 -0.4425 -0.9193 -0.2841 -0.3168 -0.0979 0.3168 0.0979 0.9193 0.2841 1.4318 0.4425 1.8042 0.5575 2.0000 0.6180 Column 11 0.0000 0.0000 -0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0 0 -0.0000 -0.0000 -0.0000 0.0000 -0.0000 -0.0000

-1.7159 -1.9021 -1.9021 -1.7159 -1.3618 -0.8743 -0.3013 0.3013 0.8743 1.3618 1.7159 1.9021

-1.4596 -1.6180 -1.6180 -1.4596 -1.1584 -0.7437 -0.2563 0.2563 0.7437 1.1584 1.4596 1.6180

-1.0605 -1.1756 -1.1756 -1.0605 -0.8416 -0.5404 -0.1862 0.1862 0.5404 0.8416 1.0605 1.1756

一维抛物方程的初边值问题

-0.0000 -0.0000 0.0000 -0.0000

T=1.5 时：>> fwave(10,0.1,30,0.05,0,2) ans = Columns 1 through 5 0 1.9021 0 1.9021 0 1.7159 0 1.3618 0 0.8743 0 0.3013 0 -0.3013 0 -0.8743 0 -1.3618 0 -1.7159 0 -1.9021 0 -1.9021 0 -1.7159 0 -1.3618 0 -0.8743 0 -0.3013 0 0.0979 0.1862 0.2563 -0.0979 -0.1862 -0.2563 -0.2841 -0.5404 -0.7437 -0.4425 -0.8416 -1.1584 -0.5575 -1.0605 -1.4596 -0.6180 -1.1756 -1.6180 -0.6180 -1.1756 -1.6180 -0.5575 -1.0605 -1.4596 -0.4425 -0.8416 -1.1584 -0.2841 -0.5404 -0.7437 -0.0979 -0.1862 -0.2563 0.0979 0.1862 0.2563 0.2841 0.5404 0.7437 0.4425 0.8416 1.1584 0.5575 1.0605 1.4596 0.6180 1.1756 1.6180 0.6180 1.1756 1.6180

T=2.0 时：fwave(10,0.1,40,0.05,0,2) ans = Columns 1 through 5 0 1.9021 0 1.9021 0 1.7159 0 1.3618 0 0.8743 0 0.3013 0 -0.3013 0 -0.8743 0 -1.3618 0 -1.7159 0 -1.9021 0 -1.9021 0 -1.7159 0 -1.3618 0 -0.8743 0 -0.3013 0 0.0979 0.1862 0.2563 -0.0979 -0.1862 -0.2563 -0.2841 -0.5404 -0.7437 -0.4425 -0.8416 -1.1584 -0.5575 -1.0605 -1.4596 -0.6180 -1.1756 -1.6180 -0.6180 -1.1756 -1.6180 -0.5575 -1.0605 -1.4596 -0.4425 -0.8416 -1.1584 -0.2841 -0.5404 -0.7437 -0.0979 -0.1862 -0.2563 0.0979 0.1862 0.2563 0.2841 0.5404 0.7437 0.4425 0.8416 1.1584 0.5575 1.0605 1.4596 0.6180 1.1756 1.6180 0.6180 1.1756 1.6180

一维抛物方程的初边值问题

0.3013 0 0.8743 0 1.3618 0 1.7159 0 1.9021 0 1.9021 0 1.7159 0 1.3618 0 0.8743 0 0.3013 0 -0.3013 0 -0.8743 0 -1.3618 0 -1.7159 0 -1.9021 Columns 6 through 10 2.0000 0.6180 2.0000 0.6180 1.8042 0.5575 1.4318 0.4425 0.9193 0.2841 0.3168 0.0979 1.9021 1.9021 1.7159 1.3618 0.8743 0.3013 1.6180 1.6180 1.4596 1.1584 0.7437 0.2563 1.1756 1.1756 1.0605 0.8416 0.5404 0.1862 -0.6180 -1.1756 -1.6180 -0.5575

-1.0605 -1.4596 -0.4425 -0.8416 -1.1584 -0.2841 -0.5404 -0.7437 -0.0979 -0.1862 -0.2563 0.0979 0.1862 0.2563 0.2841 0.5404 0.7437 0.4425 0.8416 1.1584 0.5575 1.0605 1.4596 0.6180 1.1756 1.6180 0.6180 1.1756 1.6180 0.5575 1.0605 1.4596 0.4425 0.8416 1.1584 0.2841 0.5404 0.7437

0.3013 0 0.8743 0 1.3618 0 1.7159 0 1.9021 0 1.9021 0 1.7159 0 1.3618 0 0.8743 0 0.3013 0 -0.3013 0 -0.8743 0 -1.3618 0 -1.7159 0 -1.9021 0 -1.9021 0 -1.7159 0 -1.3618 0 -0.8743 0 -0.3013 0 0.3013 0 0.8743 0 0.4425 0.8416 1.1584 0.2841 0.5404 0.7437 0.0979 0.1862 0.2563 -0.0979 -0.1862 -0.2563 -0.2841 -0.5404 -0.7437 -0.4425 -0.8416 -1.1584 -0.5575 -1.0605 -1.4596 -0.6180 -1.1756 -1.6180 -0.6180 -1.1756 -1.6180 -0.5575 -1.0605 …… 此处隐藏：7976字，全部文档内容请下载后查看。喜欢就下载吧 ……