Two-Point Boundary Value Problems - Numerical Methods in Engineering with MATLAB - page 307

If we are right, then y (0)

<

0 and y (0)

>

0.Based on this rather scantyinformation,

wetry y (0) 1 and y (0)

1.
The following program uses the adaptive Runge-Kuttamethod ( runKut5 )for
integration:

=− =

function shoot4nl
% Shooting method for nonlinear 4th-order boundary
% value problem in Example 8.5.

global XSTART XSTOP H % Make these params. global.

XSTART = 0; XSTOP = 1; % Range of integration.

H = 0.1; % Step size.

freq = 1; % Frequency of printout.

u=[-11]; %Trialvaluesofu(1)

% and u(2).

x = XSTART;
u = newtonRaphson2(@residual,u);
[xSol,ySol] = runKut5(@dEqs,x,inCond(u),XSTOP,H);
printSol(xSol,ySol,freq)

functionF=dEqs(x,y) %Differentialequations.

F = zeros(1,4);
F(1) = y(2); F(2) = y(3); F(3) = y(4);
ifx<10.0e-4;F(4)=-12*y(2)*y(1)ˆ2;
else; F(4) = -4*(y(1)ˆ3)/x;

end

functiony=inCond(u) %Initialconditions;u(1)

y = [0 0 u(1) u(2)]; % and u(2) are unknowns.

functionr=residual(u) %Boundayresiduals.
global XSTART XSTOP H
r = zeros(length(u),1);
x = XSTART;
[xSol,ySol] = runKut5(@dEqs,x,inCond(u),XSTOP,H);
lastRow = size(ySol,1);
r(1) = ySol(lastRow,3);
r(2) = ySol(lastRow,4) - 1;