Difference between bvp4c and ode15s

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Joshua 2012-7-13

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/43593-difference-between-bvp4c-and-ode15s

Hi, I'm getting differing results from bvp4c and ode15s. I've used bvp4c to produce an estimate of the solution to a set of equations. I've then used the initial conditions for this given solution and plugged it into ode15s. However, when I compare the results, they look nothing alike. Am I doing something wrong?

This function produces a 2x2 plot with the top pair being the results of the bvp4c and the bottom pair being the results of ode15s. Theoretically, they should be the same.

Any help would be appreciated. Thanks!

function [sol T Y] = fhn4bvp
solinit = bvpinit(linspace(0, 30, 250), @fhn4init);
sol = bvp4c(@fhn4ode, @fhn4bc, solinit);
figure; 
subplot(2, 2, 1); plot(sol.x, sol.y(1, :) / 2);
subplot(2, 2, 2); plot(sol.y(3, :), sol.y(4, :)); axis([-2 2 -0.6 1.5])
% putting it back into the FHN
[T Y] = ode15s(@(t, y) fhn4ode(t, y), [0 30], [sol.y(1, 1) sol.y(2, 1) sol.y(3, 1), sol.y(4, 1)]);
%[T Y] = ode15s(@(t, y) fhn(t, y, sol.x, sol.y(1, :) / 2), [0 30], [0.95836586 -0.322958325]);
subplot(2, 2, 3); plot(T, Y(:, 1));
subplot(2, 2, 4); plot(Y(:, 3), Y(:, 4));
function res = fhn4bc(ya,yb)
    res = [ ya(3) - 0.95836586
            ya(4) + 0.322958325
            yb(3) - 0.8909
            yb(4) + 0.4062 ];
function yinit = fhn4init(x)
    amp = 0.000;
    yinit = [ amp * cos( 2 * pi * x / 15 )
              amp * sin( 2 * pi * x / 15 ) 
              amp * cos( 2 * pi * x / 15 )
              amp * sin( 2 * pi * x / 15 ) ];
% lambda_x = y(1); lambda_y = y(2); x = y(3); y = y(4)          
function fhnsol = fhn4ode(t, y)
a = 0.7; b = 0.8; c = 3.0; r = 0.342;
fhnsol = [ -c * (1 - y(3)^2) * y(1) + y(2) / c
           -c * y(1) + b * y(2) / c
           c * (y(4) + y(3) - y(3)^3 / 3 - r) + y(1) / 2
           -(y(3) - a + b * y(4)) / c ];