Question

MATLAB CODE: Making cubic spline iterpolation function. Then, To solve use Tridiagonal matrix algorithm(TDMA)

xi	-0.5	-0.4	-0.2	0	0.2	0.4	0.6	0.8
yi	0.04	0.1	0.4	1	0.35	0.2	0.3	0.04

Answer 1

hi first write the xi and yi in given format -

#ans.m

xi=[-0.5 -0.4 ...... 0.8];

yi=[0.04 0.1 ........ 0.04];

xii=linspace(-0.5 0.8 20);

yii=spline(xi,yi,xii); %%cubic spline command interpolate to xii points..

then use unmkpp command to get the coefficients..

these coeeficient will be in matrix shown below function.put syntax as per your own..

%%now for solving using tridiagonal matrix algorithm -

function y = tridiag( a, b, c, f )

%  Solve the  n x n  tridiagonal system for y:
%
%  [ a(1)  c(1)                                  ] [  y(1)  ]   [  f(1)  ]
%  [ b(2)  a(2)  c(2)                            ] [  y(2)  ]   [  f(2)  ]
%  [       b(3)  a(3)  c(3)                      ] [        ]   [        ]
%  [            ...   ...   ...                  ] [  ...   ] = [  ...   ]
%  [                    ...    ...    ...        ] [        ]   [        ]
%  [                        b(n-1) a(n-1) c(n-1) ] [ y(n-1) ]   [ f(n-1) ]
%  [                                 b(n)  a(n)  ] [  y(n)  ]   [  f(n)  ]
%
%  f must be a vector (row or column) of length n
%  a, b, c must be vectors of length n (note that b(1) and c(n) are not used)

% some additional information is at the end of the file

n = length(f);
v = zeros(n,1);   
y = v;
w = a(1);
y(1) = f(1)/w;
for i=2:n
    v(i-1) = c(i-1)/w;
    w = a(i) - b(i)*v(i-1);
    y(i) = ( f(i) - b(i)*y(i-1) )/w;
end
for j=n-1:-1:1
   y(j) = y(j) - v(j)*y(j+1);
end

ref: Mathworks/help/matlab