I am trying to solve Nonlinear systems of equations using Newton-Raphson method, having problem while using newtmult function. Please guide me to correct my code.
function [J,f]=jfreact(x,varargin)
del=0.000001;
df1dx1=(u(x(1)+del*x(1),x(2))-u(x(1),x(2)))/(del*x(1));
df1dx2=(u(x(1),x(2)+del*x(2))-u(x(1),x(2)))/(del*x(2));
df2dx1=(v(x(1)+del*x(1),x(2))-v(x(1),x(2)))/(del*x(1));
df2dx2=(v(x(1),x(2)+del*x(2))-v(x(1),x(2)))/(del*x(2));
J=[df1dx1 df1dx2;df2dx1 df2dx2];
f1=u(x(1),x(2));
f2=v(x(1),x(2));
f=[f1;f2];
function f=u(x,y)
f = (5 + x + y) / (50 – 2 * x – y) ^ 2 / (20 – x) – 0.0004;
function f=v(x,y)
f = (5 + x + y) / (50 – 2 * x – y) / (10 – y) – 0.037;
solver function used:- (Initial guesses are x1=x2=3)
function [x,f,ea,iter]= newtmult(@jfreact,[3;3],es,maxit,varargin);
es=50;
if nargin<2,error(‘at least 2 input arguments required’),end
if nargin<3||isempty(es),es=0.0001;end
if nargin<4||isempty(maxit),maxit=50;end
iter = 0;
x=x0;
while (1)
[J,f]=jfreact(x,varargin{:});
dx=Jf;
x=x-dx;
iter = iter + 1;
ea=100*max(abs(dx./x));
if iter>=maxit||ea<=es, break, end
end
endfunction [J,f]=jfreact(x,varargin)
del=0.000001;
df1dx1=(u(x(1)+del*x(1),x(2))-u(x(1),x(2)))/(del*x(1));
df1dx2=(u(x(1),x(2)+del*x(2))-u(x(1),x(2)))/(del*x(2));
df2dx1=(v(x(1)+del*x(1),x(2))-v(x(1),x(2)))/(del*x(1));
df2dx2=(v(x(1),x(2)+del*x(2))-v(x(1),x(2)))/(del*x(2));
J=[df1dx1 df1dx2;df2dx1 df2dx2];
f1=u(x(1),x(2));
f2=v(x(1),x(2));
f=[f1;f2];
function f=u(x,y)
f = (5 + x + y) / (50 – 2 * x – y) ^ 2 / (20 – x) – 0.0004;
function f=v(x,y)
f = (5 + x + y) / (50 – 2 * x – y) / (10 – y) – 0.037;
solver function used:- (Initial guesses are x1=x2=3)
function [x,f,ea,iter]= newtmult(@jfreact,[3;3],es,maxit,varargin);
es=50;
if nargin<2,error(‘at least 2 input arguments required’),end
if nargin<3||isempty(es),es=0.0001;end
if nargin<4||isempty(maxit),maxit=50;end
iter = 0;
x=x0;
while (1)
[J,f]=jfreact(x,varargin{:});
dx=Jf;
x=x-dx;
iter = iter + 1;
ea=100*max(abs(dx./x));
if iter>=maxit||ea<=es, break, end
end
end function [J,f]=jfreact(x,varargin)
del=0.000001;
df1dx1=(u(x(1)+del*x(1),x(2))-u(x(1),x(2)))/(del*x(1));
df1dx2=(u(x(1),x(2)+del*x(2))-u(x(1),x(2)))/(del*x(2));
df2dx1=(v(x(1)+del*x(1),x(2))-v(x(1),x(2)))/(del*x(1));
df2dx2=(v(x(1),x(2)+del*x(2))-v(x(1),x(2)))/(del*x(2));
J=[df1dx1 df1dx2;df2dx1 df2dx2];
f1=u(x(1),x(2));
f2=v(x(1),x(2));
f=[f1;f2];
function f=u(x,y)
f = (5 + x + y) / (50 – 2 * x – y) ^ 2 / (20 – x) – 0.0004;
function f=v(x,y)
f = (5 + x + y) / (50 – 2 * x – y) / (10 – y) – 0.037;
solver function used:- (Initial guesses are x1=x2=3)
function [x,f,ea,iter]= newtmult(@jfreact,[3;3],es,maxit,varargin);
es=50;
if nargin<2,error(‘at least 2 input arguments required’),end
if nargin<3||isempty(es),es=0.0001;end
if nargin<4||isempty(maxit),maxit=50;end
iter = 0;
x=x0;
while (1)
[J,f]=jfreact(x,varargin{:});
dx=Jf;
x=x-dx;
iter = iter + 1;
ea=100*max(abs(dx./x));
if iter>=maxit||ea<=es, break, end
end
end non linear equations, newton raphson method, iteration MATLAB Answers — New Questions
