What is the meaning of the error?

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Zeynep Toprak 2020-5-8

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https://ww2.mathworks.cn/matlabcentral/answers/524081-what-is-the-meaning-of-the-error

评论： Zeynep Toprak 2020-5-17

在 MATLAB Online 中打开

Question is from Tobin's book.

For part (a)'s matlab code and result,

n = 100 ; h = 2/n; %n intervals, width 2/n
x = -1 + h* (1: n-1)'; %node locations
D2 = toeplitz ([-2 1 zeros(1, n-3)]/ h^2); %diff matrix for u_xx 
f = @(t, u) (0.2*D2*u ) + u.^2; % discretized du/dt
u0 = (1 - x.^2) ./ (1 + 50*x.^2); %initial condition
[t, u] = ode15s (f, [0 2], u0); %solve
waterfall (x, t, u) 

And for part (b),

n = 100 ; h = 2/n; %n intervals, width 2/n
x = -1 + h* (1: n-1)'; %node locations
D2 = toeplitz ([-2 1 zeros(1, n-3)]/ h^2); %diff matrix for u_xx 
f = @(t, u) (0.2*D2*u ) + u.^2; % discretized du/dt
u0 = 10 * (1 - x.^2) ./ (1 + 50*x.^2); %initial condition
[t, u] = ode15s (f, [0 2], u0); %solve
waterfall (x, t, u) 

I get the following error when I run the code for the part b,

Warning: Failure at t=1.993395e-01.  Unable to meet integration tolerances without reducing the step size below the smallest value
allowed (4.440892e-16) at time t. 
> In ode15s (line 730)
  In exercise_714_part_b (line 13) 

I also get the following graph for the part b

Why did I face this error message? What is the meaning of it? and how can I correct it? Where is my mistake? And The graph for the part b is a bit nonsense. I cannot interpret this part and the graph.

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Gokberk Yildirim 2020-5-16

Zeynep if you decrease the tolerance of time t, this graph will work without any warning. For example, you can change this part [t, u] = ode15s (f, [0 2], u0) like this [t, u] = ode15s (f, [0 0.1], u0). It gives us enough tolerance for calculation of integration in ode15s.

Zeynep Toprak 2020-5-17