Problem with solving an ODE

Question

Della 2023-5-17

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1966519-problem-with-solving-an-ode

回答： Torsten 2023-5-17

Hello,

When I run the code below, I get an error because the initial condition for y is dependent on Dy. I've seen this case (boundary conditions depend on first derivatives) in a few papers, but I'm not sure how to solve it. Could someone please help me with this?

syms y Dy D2y x Y

y0=(5+Dy*2)/0.49;

ode = y-(1/(Dy/y+(D2y*x)/y))^2;

ode1 = solve(ode==0,D2y)

ode1 =

ode2 = matlabFunction(ode1(1),'Vars',{x,[y Dy]})

ode2 = function_handle with value:

@(x,in2)(in2(:,1).*(sqrt(1.0./in2(:,1))-in2(:,2)./in2(:,1)))./x

odefcn = @(x,y)[y(2);ode2(x,[y(1),y(2)])];

bcfcn = @(ya,yb)[ya(1)-y0;yb(2)-1];

xmesh = linspace(1e-3,4,10);

solinit = bvpinit(xmesh, [1 1]);

sol = bvp4c(odefcn,bcfcn,solinit);

Unable to perform assignment because value of type 'sym' is not convertible to 'double'.

Error in bvp4c>colloc_RHS (line 543)
Phi(1:nBCs) = Gbc(y(:,Lidx),y(:,Ridx),ExtraArgs{1:nExtraArgs});

Error in bvp4c (line 182)
[RHS,yp,Fmid,NF] = colloc_RHS(n,x,Y,ode,bc,npar,xyVectorized,mbcidx,nExtraArgs,ExtraArgs);

Caused by:
Error using symengine
Unable to convert expression containing symbolic variables into double array. Apply 'subs' function first to substitute values for variables.

plot(sol.x,sol.x.*sol.y(1,:))