MATLAB solving BVP using bvp4c

Question

Taylor Nichols 2018-10-4

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/422259-matlab-solving-bvp-using-bvp4c

评论： Torsten 2018-10-5

I am trying to solve a BVP in matlab using the bvp4c function. The following equation is a 3rd order linear homogeneous ODE with constant coefficients. I have solved second order linear and non-linear but I can't seem to figure out how to do a third order. I cannot find and documentation on how to make this adjustment.

The equation: y''' = a*h'

with boundary conditions y(0) = 0.3; y(15) = 0.7; y'(0) = 0;

The main code I have tried is below:

init = bvpinit(linspace(1,15,10),[0,0]);
sol = bvp4c(@rhs_bvp, @bc_bvp, init);
x = linspace(1,15,100);
BS = deval(sol, x);
plot(x,BS(1,:));

using the bc_bvp funtion below:

function [ bc ] = bc_bvp( yl, yr )
hi = 0.3;
ho = 0.7;
bc = [yl(1) - hi; 
      yl(2);
      yr(1) - ho];
end

and the rhs_bvp function below:

function [ rhs ] = rhs_bvp( x, y )
a = 26;
rhs = [y(3); a*y(2)];
end

and I get this error:

    Index exceeds matrix dimensions.
    Error in rhs_bvp (line 8)
    rhs = [y(3); a*y(2)];
    Error in bvparguments (line 105)
        testODE = ode(x1,y1,odeExtras{:});
    Error in bvp4c (line 130)
        bvparguments(solver_name,ode,bc,solinit,options,varargin);

Any help would be greatly appreciated.

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Torsten 2018-10-5

What is h' ?

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Answer 1

Torsten 2018-10-5

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/422259-matlab-solving-bvp-using-bvp4c#answer_339856

在 MATLAB Online 中打开

If h' = y', try

function main
init = bvpinit(linspace(1,15,10),[0,0,0]);
sol = bvp4c(@rhs_bvp, @bc_bvp, init);
x = linspace(1,15,100);
BS = deval(sol, x);
plot(x,BS(1,:));
end
function [ rhs ] = rhs_bvp( x, y )
a = 26;
rhs = [y(2); y(3); a*y(2)];
end
function [ bc ] = bc_bvp( yl, yr )
hi = 0.3;
ho = 0.7;
bc = [yl(1) - hi; 
      yl(2);
      yr(1) - ho];
end

Best wishes

Torsten.

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Taylor Nichols 2018-10-5

Thanks for the help Torsten! I guess including a picture of how I broke down the function would've helped. So if we have a 3rd order function we need to have 3 initial guesses? I'm also confused on why we set up the rhs variable that way too. I have only seen examples on 2nd order. And no detailed documentation on using this method exist. If you have anymore quick pointers it would be greatly appreciated!