nlineq_driver.m

nonlinear eq routines in matlab

%
%  nlineq_driver.m
% 
%  use bisect.m and newt1d.m to compute an approximation
%  of the root of  f(x) = cos(x)*cosh(x)+1
%
%  Matthias Heinkenschloss
%  Department of Computational and Applied Mathematics
%  Rice University
%



disp(' ')
disp(' Find the root of f(x) = cox(x)*cosh(x)+1 ')
disp(' ')
disp(' Hit return to continue with the Bisection Method')
disp(' ')
pause
f     = 'coscosh';
a     = 1.6;
b     = 2;
tolx  = 1.e-7;

[a, b, x, ithist, iflag] = bisect( f, a, b, tolx );
fprintf('\n  The Bisection Method returned with iflag = %d \n ', iflag)

fprintf('\n  Bisection Method \n ')
fprintf(' iter         a              b              c            f(c) \n ')
for i = 1:size(ithist,1)
   fprintf('%4d &$ %13.8e $&$ %13.8e $&$ %13.8e $&$ %13.8e $\\\\ \n ', ithist(i,:))
end


disp(' ')
disp(' Hit return to continue with Regula Falsi')
disp(' ')
pause
a     = 1.6;
b     = 2;
tolf  = 1.e-14;
[a, b, x, ithist, iflag] = regulafalsi( f, a, b, tolf );
fprintf('\n  Regula falsi returned with iflag = %d \n ', iflag)

fprintf('\n  Regula Falsi \n ')
fprintf(' iter         a              b              c            f(c) \n ')
for i = 1:size(ithist,1)
   fprintf('%4d &$ %13.8e $&$ %13.8e $&$ %13.8e $&$ %13.8e $\\\\ \n ', ithist(i,:))
end


disp(' ')
disp(' Hit return to continue with Newton''s Method')
disp(' ')
pause

x = 2;
[x, ithist, iflag] = newt1d( f, x, 1.e-15, 1.e-15, 20 );
fprintf('\n  Newton''s Method returned with iflag = %d \n ', iflag)

fprintf('\n  Newton''s Method \n ')
fprintf(' iter        x             f(x)          -f(x)/f''(x)  \n ')
for i = 1:size(ithist,1)
   fprintf('%4d &$ %13.8e $&$ %13.8e $&$ %13.8e $\\\\ \n ', ithist(i,:))
end



disp(' ')
disp(' Hit return to continue with Secant Method')
disp(' ')
pause

x = 2; x1 = 2.01
[x, ithist, iflag] = secant( f, x, x1, 1.e-15, 1.e-15, 20 )

fprintf('\n  Secant Method returned with iflag = %d \n ', iflag)

fprintf('\n  Secant Method \n ')
fprintf(' iter        x             f(x)          -f(x)/f''(x)  \n ')
for i = 1:size(ithist,1)
   fprintf('%4d &$ %13.8e $&$ %13.8e $&$ %13.8e $\\\\ \n ', ithist(i,:))
end




disp(' ')
disp(' Hit return to continue with Newton''s Method')
disp(' ')
pause

f = 'xsinx2';

x = 0.5;
[x, ithist, iflag] = newt1d( f, x, 1.e-12, 1.e-15, 20 );
fprintf('\n  Newton''s Method returned with iflag = %d \n ', iflag)

fprintf('\n  Newton''s Method \n ')
fprintf(' iter        x             f(x)          -f(x)/f''(x)  \n ')
for i = 1:size(ithist,1)
   fprintf('%4d &$ %13.8e $&$ %13.8e $&$ %13.8e $\\\\ \n ', ithist(i,:))
end