内容简介作者简介 - 科学与工程计算系

2.5
2
1.5
1
0.5
0
-0.5
-1
-1.5
插值后的解曲线
解点
猜测解点
-2
0 0.5 1 1.5 2 2.5 3 3.5 4
图 4.14-5
4.14.5.3 改善边值问题的求解性能
【例 4.14.5.3-1】求解微分方程 z′ ′ + ( λ − 2q
cos2x)
z = 0 ,在此令 q = 15 。边界条件为
z ( 0)
= 1,
z′
( 0)
= 0,
z′
( π ) = 0 。本例的目的:(A)演示含未知参数微分方程边值问题的求
解;(B)边界条件的数学表达和 M 函数文件的编写;(C)函数型猜测解的构成方式;(D)
使用 bvpset 改变选项属性;(E)采用构架直接赋值法改变选项属性。(F)演示“接续”
求解法。
(1)
(2)
[mat4ode.m]
function dydx=mat4ode(x,y,lmb)
q=5;
dydx=[y(2); -(lmb – 2*q*cos(2*x))*y(1)];
[mat4bc.m]
function res=mat4bc(ya,yb,lmb)
res=[ ya(1)-1 ; ya(2) ; yb(2) ];
(3)
clear
x00=linspace(0,pi,4); %
y00=inline('[cos(4*x);-4*sin(4*x)]'); %
lmb=15; %
s0=bvpinit(x00,y00,lmb); %
(4)
opts=bvpset('AbsTol',0.5,'RelTol',0.38,'Stats','on');%
s1= bvp4c(@mat4ode,@mat4bc,s0,opts); %
Lambda1=s1.parameters
The solution was obtained on a mesh of 7 points.
The maximum residual is 1.263e-001.
There were 356 calls to the ODE function.
There were 67 calls to the BC function.
Lambda1 =
40