1 / 34

# 第十章 常微分方程数值解 - PowerPoint PPT Presentation

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about '第十章 常微分方程数值解' - ros

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

(10-1)

x0

x1

1. 数值微分法,用差商代替微商

2. Taylor展开法

3. 数值积分法区间

x0

x1

+

y

(

x

)

y

h

f

(

x

,

y

(

x

))

1

0

1

1

y

y

y

+

+

+

1

1

1

n

n

n

=

+

Step 1:先用显式欧拉公式作预测，算出

y

h

f

(

x

,

y

)

n

n

n

Step 2: 再将 代入隐式梯形公式的右边作校正，得到

x0

x1

x2

h

=

+

+

y

y

[

f

(

x

,

y

)

f

(

x

,

)]

+

+

1

1

n

n

n

n

n

2

— 显、隐式两种算法的平均

1. 整体截断误差和局部截断误差

若某算法的局部截断误差为 ，则称该算法有p阶精度。

2. 收敛性和整体截断误差

0.0

0.1

0.2

0.3

0.4

0.5

3. 稳定性

1.0000

2.0000

4.0000

8.0000

1.6000101

3.2000101

1.0000

2.5000101

6.2500102

1.5625102

3.9063103

9.7656104

1.0000

2.5000

6.2500

1.5626101

3.9063101

9.7656101

1.0000

4.9787102

2.4788103

1.2341104

6.1442106

3.0590107

=

l h

h

h

Img

-

2

-

1

0

Re

Img

0

1

2

Re