bvptest.asv

(有源代码)数值分析作业,本文主要包括两个部分,第一部分是常微分方程(ODE)的三个实验题,第二部分是有关的拓展讨论,包括高阶常微分的求解和边值问题的求解(BVP).文中的算法和算例都是基于Matla

% function bvptest
solinit = bvpinit([0 1 2 3 4],[1; 0]);
sol = bvp4c(@twoode, @twobc, solinit);

xint = linspace(0, 4, 50);
yint = deval(sol, xint);
plot(xint, yint(1,:),'b');
xlabel('x')
ylabel('solution y')
% hold on

%%
% This particular boundary value problem has exactly two solutions.  The other
% solution is obtained for an initial guess of 
% 
%     y(x) = -1, y'(x) = 0 
% 
% and plotted as before.
figure
hold on

solinit = bvpinit([0 1 2 3 4],[100; 0]);
sol = bvp4c(@twoode,@twobc,solinit);

xint = linspace(0,4,50);
yint = deval(sol,xint);
plot(xint,yint(1,:),'r');

legend('sol','solinit')
title('BVP')