MATLAB: Not spotting where/how index exceeds number of array elements

array elementsexceedsindex

I'm trying to solve a Navier-Stokes setup in a cylindrical coordinate system and am bumping up against an array indexing challenge. Any help folks might be able to offer to straighten matters out would be most appreciated. I'm including my live editor content below.

Best Answer

Is this what you want? Live script vesion is attached.

xmesh = linspace(0.01,0.05,5);
solinit = bvpinit(xmesh, @guess);
sol = bvp4c(@bvpfcn, @bcfcn, solinit);
plot(sol.x, sol.y, '-o')
function bound = bcfcn(ua,ub)
bound = [ua(1)-0.1, ub(1)];
end
function g = guess(r)
g = [1*(0.05-r)/(0.05-0.01), -1/(0.05-0.01)];
end
function dudr = bvpfcn(r,u)
dudr = [u(2), u(2)./r];
end

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MATLAB: Solving 4th order ode

Use bvp4c()

You already have written your equation as system of first-order equations

function dydt = ode4(t,y)
    L=1;B=0.25;k=0.1;
    dydt = zeros(4,1);
    dydt(1)=y(2);
    dydt(2)=y(3);
    dydt(3)=y(4);
    dydt(4)=(2.*B+1+y(1)).*y(3))./(k.*(1+y(1));
end

Here is function for your boundary conditions

function res = bc4(y0, y1)
    res = [y0(1)-0        % y(0) = 0
           y0(2)-1        % y'(0) = 1
           y1(1)-0        % y(end) = 0
           y1(2)-1];      % y'(end) = 1
end

See bvp4c

MATLAB: How to solve this BVP problem which is second-order ODE with variable coefficient

Your function handle appears to be incorrect:

syms y(x)
eq = diff(y,x,2) + ((1-10*x^2)/x)*diff(y,x,1) == 0;
[V,S] = odeToVectorField(eq);
fun = matlabFunction(V,'Vars',{'x','Y'})

gives:

fun =
  function_handle with value:
    @(x,Y)[Y(2);((x.^2.*1.0e+1-1.0).*Y(2))./x]

additionally your function gets singular at x=0, to avoid this:

fun = @(x,Y)[Y(2);((x.^2.*1.0e+1-1.0).*Y(2))./x];
bc = @(ya, yb) [ya(1) - 1; yb(1)];
xmesh = linspace(1e-4, 1, 100);
solinit = bvpinit(xmesh, [1 0]);
sol = bvp4c(fun, bc, solinit);
figure;
yyaxis left
plot(sol.x, sol.y(1,:),'LineWidth',2)
yyaxis right
semilogy(sol.x, sol.y(2,:),'LineWidth',2)

Note that the right axis is log scaled:

Best Answer

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MATLAB: Solving 4th order ode

MATLAB: How to solve this BVP problem which is second-order ODE with variable coefficient

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