%--
%-- matlab script to reproduce table 1.1, textbook 
%-- 
%-- Finite Difference Methods for Ordinary and Partial
%-- Differential Equations by Randall J. LeVeque
%--
%-- By Nasser M. Abbasi   oct 5, 2010
%-- Math 228A, UC DAVIS, Fall 2010

    h=[0.1 0.05 0.01 0.005 0.001];
    exact_value = cos(1);
    result= zeros(4,1);

    derivative_left  = @(h) (sin(1) - sin(1-h))/h;
    derivative_right = @(h) (sin(1+h) - sin(1))/h;
    derivative_center = @(h) (sin(1+h) - sin(1-h))/(2*h);
    derivative_3rd_order = @(h) (2*sin(1+h)+3*sin(1)-6*sin(1-h) ...
                                 +sin(1-2*h))/(6*h);
                             
    fprintf(strcat('%s\t',repmat('%s\t\t',1,4),'\n'),...
                    '   h','D+','D_','D0','D3');
                
    for i=1:length(h)
     result(1) = derivative_right(h(i))     -  exact_value; 
     result(2) = derivative_left(h(i))      -  exact_value;
     result(3) = derivative_center(h(i))    -  exact_value; 
     result(4) = derivative_3rd_order(h(i)) -  exact_value;
     fprintf(strcat('%3.1E\t',repmat('%6.4E\t',1,4),'\n'),h(i),result);
    end