mat lab problem

[von ski]

Hi below is matlab code for the boundary value problem y'''' + yy'' + x2 cos (pi(y)) -1 = 0; y(-1) = 0; y(1) = 0; y'(-1) = 1; y'(1) = 1:


I want the code to display a matrix SOL whose columns are successive approximations
to the solution. But the matrix just isn't showing up...can anyone see why.

Thanks


% This is a boilerplate code to calculate the solution to a
% nonlinear BVP of fourth order, two dirichlet and two neumann BCs
% Define the interval over which solution is calculated
a= -1;
b= 1;
% Define N
N=100;
% Define the grid spacing
h=(b-a)/N;
% Define the grid
x= reshape ( linspace (a,b,N+1) ,N+1 ,1);
% Define an initial guess for the solution of the BVP (make sure it
% is a column vector)
U=x.*(1-x);
% Store the initial guess in SOL
SOL =U;
% Define a tolerance for the termination of Newton?Raphson
tol =1e-4;
% Ensure that F is such that we always do at least one iteration
F= ones (N+1 ,1);J= zeros (N+1,N +1);
% The loop continues while ever the norm of F is greater than tol
while ( norm (F)>tol)
%% Define F
% Boundary conditions
F (1)= U(1) ;
F(N +1)=U(N+1);
% Boundary conditions (Fictitious nodes) + ODE
F (2)=((3*U(1)-4*U(2)-U(3)+2*h)/h^2) - (1-x(1));
F(N)=((3*U(N+1)-4*U(N)+U(N-1)-2*h)/h^2)-(1-x(1));
% Finite difference approximation to ODE at interior nodes
for i =3N -1),
F(i)=(U(i+2)-4*U(i+1)+6*U(i)-4*U(i-1)+U(i-2))+(h^2*U(i))*(U(i+1)-2*U(i)+U(i-1))+(h^4*x(i))*(cos(pi*U(i)))-(h^4);
end
%% Define J
% First row corresponds to F(1)=...;
J (1 ,1)=1;
% Last row corresponds to F(N+1)=...;
J(N +1 ,N+1)=1;
% Second row corresponds to F(2)=...;
J (2 ,1)=3/h^2;
J (2 ,2)=-4/h^2;
J (2 ,3)=-1/h^2;
% Penultimate row corresponds to F(2)=...;
J(N ,N-1)=1/h^2;
J(N ,N)=-4/h^2;
J(N ,N+1)=3/h^2;
% Intermediate rows correspond to F(i)=...;
for i =3N -1) ,
% Diagonal entry
J(i,i)=6-2*h^2*U(i)^2 +h^4*x(i)*cos(pi*U(i));
J(i,i-2)=1;
J(i,i-1)=-4+h^2*U(i)*U(i-1);
J(i,i+1)=-4+h^2*U(i)*U(i+1);
J(i,i+2)=1;
% There may be off?diagonal entries, check your calculation
end
% Having defined F and J, update the approximate solution to
% difference equations
U=U-J\F;
% Store the new approximation
SOL =[ SOL ,U];
end
plot(x,U);
% Insert your plot command

 

[Deleted member 4993]

Hi below is matlab code for the boundary value problem y'''' + yy'' + x2 cos (pi(y)) -1 = 0; y(-1) = 0; y(1) = 0; y'(-1) = 1; y'(1) = 1:


I want the code to display a matrix SOL whose columns are successive approximations
to the solution. But the matrix just isn't showing up...can anyone see why.

Thanks


% This is a boilerplate code to calculate the solution to a
% nonlinear BVP of fourth order, two dirichlet and two neumann BCs
% Define the interval over which solution is calculated
a= -1;
b= 1;
% Define N
N=100;
% Define the grid spacing
h=(b-a)/N;
% Define the grid
x= reshape ( linspace (a,b,N+1) ,N+1 ,1);
% Define an initial guess for the solution of the BVP (make sure it
% is a column vector)
U=x.*(1-x);
% Store the initial guess in SOL
SOL =U;
% Define a tolerance for the termination of Newton?Raphson
tol =1e-4;
% Ensure that F is such that we always do at least one iteration
F= ones (N+1 ,1);J= zeros (N+1,N +1);
% The loop continues while ever the norm of F is greater than tol
while ( norm (F)>tol)
%% Define F
% Boundary conditions
F (1)= U(1) ;
F(N +1)=U(N+1);
% Boundary conditions (Fictitious nodes) + ODE
F (2)=((3*U(1)-4*U(2)-U(3)+2*h)/h^2) - (1-x(1));
F(N)=((3*U(N+1)-4*U(N)+U(N-1)-2*h)/h^2)-(1-x(1));
% Finite difference approximation to ODE at interior nodes
for i =3N -1),
F(i)=(U(i+2)-4*U(i+1)+6*U(i)-4*U(i-1)+U(i-2))+(h^2*U(i))*(U(i+1)-2*U(i)+U(i-1))+(h^4*x(i))*(cos(pi*U(i)))-(h^4);
end
%% Define J
% First row corresponds to F(1)=...;
J (1 ,1)=1;
% Last row corresponds to F(N+1)=...;
J(N +1 ,N+1)=1;
% Second row corresponds to F(2)=...;
J (2 ,1)=3/h^2;
J (2 ,2)=-4/h^2;
J (2 ,3)=-1/h^2;
% Penultimate row corresponds to F(2)=...;
J(N ,N-1)=1/h^2;
J(N ,N)=-4/h^2;
J(N ,N+1)=3/h^2;
% Intermediate rows correspond to F(i)=...;
for i =3N -1) ,
% Diagonal entry
J(i,i)=6-2*h^2*U(i)^2 +h^4*x(i)*cos(pi*U(i));
J(i,i-2)=1;
J(i,i-1)=-4+h^2*U(i)*U(i-1);
J(i,i+1)=-4+h^2*U(i)*U(i+1);
J(i,i+2)=1;
% There may be off?diagonal entries, check your calculation
end
% Having defined F and J, update the approximate solution to
% difference equations
U=U-J\F;
% Store the new approximation
SOL =[ SOL ,U];
end
plot(x,U);
% Insert your plot command

Unfortunately, we do not have MATLAB expert among us - atleast I do not know of any.

 

[dsk2]

von ski,

You are storing the matrix, but you are not displaying it.
Remove the semicolon when you store the SOL matrix, or print out the matrix at the end of the script by typing
SOL
without the semicolon.

Cheers,
Sai.

% Store the new approximation

SOL =[ SOL ,U];