MATLAB Mathematics - SERC - Index of

5 Differential Equations
vectorized to improve solver performance. The additional parameter ε is
represented by e and is shared with the outer function.
function dydx = shockODE(x,y)
pix = pi*x;
dydx = [ y(2,:)
-x/e.*y(2,:) - pi^2*cos(pix) - pix/e.*sin(pix) ];
end % End nested function shockODE
function res = shockBC(ya,yb)
res = [ ya(1)+2
yb(1) ];
end % End nested function shockBC
2 Provide analytical partial derivatives. For this problem, the solver
benefits from using analytical partial derivatives. The code below represents
the derivatives in functions shockJac and shockBCJac.
function jac = shockJac(x,y)
jac = [ 0 1
0 -x/e ];
end % End nested function shockJac
function [dBCdya,dBCdyb] = shockBCJac(ya,yb)
dBCdya = [ 1 0
0 0 ];
dBCdyb = [ 0 0
1 0 ];
end % End nested function shockBCJac
shockJac shares e with the outer function.
Tell bvp4c to use these functions to evaluate the partial derivatives by
setting the options FJacobian and BCJacobian. Also set 'Vectorized' to
'on' to indicate that the differential equation function shockODE is
vectorized.
options = bvpset('FJacobian',@shockJac,...
'BCJacobian',@shockBCJac,...
'Vectorized','on');
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