Matlab 6 Numerical Integration Methods

quad

 QUAD   Numerically evaluate integral, adaptive Simpson quadrature.
    Q = QUAD(FUN,A,B) tries to approximate the integral of function
    FUN from A to B to within an error of 1.e-6 using recursive
    adaptive Simpson quadrature.  The function Y = FUN(X) should
    accept a vector argument X and return a vector result Y, the
    integrand evaluated at each element of X.  
 
    Q = QUAD(FUN,A,B,TOL) uses an absolute error tolerance of TOL 
    instead of the default, which is 1.e-6.  Larger values of TOL
    result in fewer function evaluations and faster computation,
    but less accurate results.  The QUAD function in MATLAB 5.3 used
    a less reliable algorithm and a default tolerance of 1.e-3.
 
    [Q,FCNT] = QUAD(...) returns the number of function evaluations.
 
    QUAD(FUN,A,B,TOL,TRACE) with non-zero TRACE shows the values
    of [fcnt a b-a Q] during the recursion.
 
    QUAD(FUN,A,B,TOL,TRACE,P1,P2,...) provides for additional 
    arguments P1, P2, ... to be passed directly to function FUN,
    FUN(X,P1,P2,...).  Pass empty matrices for TOL or TRACE to
    use the default values.
 
    Use array operators .*, ./ and .^ in the definition of FUN
    so that it can be evaluated with a vector argument.
 
    Function QUADL may be more efficient with high accuracies
    and smooth integrands.
 
    Example:
        FUN can be specified three different ways.
 
        A string expression involving a single variable:
           Q = quad('1./(x.^3-2*x-5)',0,2);
 
        An inline object:
           F = inline('1./(x.^3-2*x-5)');
           Q = quad(F,0,2);
 
        A function handle:
           Q = quad(@myfun,0,2);
           where myfun.m is an M-file:
              function y = myfun(x)
              y = 1./(x.^3-2*x-5);

quadl

 
 QUADL  Numerically evaluate integral, adaptive Lobatto quadrature.
    Q = QUADL(FUN,A,B) tries to approximate the integral of function
    FUN from A to B to within an error of 1.e-6 using high order
    recursive adaptive quadrature.  The function Y = FUN(X) should
    accept a vector argument X and return a vector result Y, the
    integrand evaluated at each element of X.  
 
    Q = QUADL(FUN,A,B,TOL) uses an absolute error tolerance of TOL 
    instead of the default, which is 1.e-6.  Larger values of TOL
    result in fewer function evaluations and faster computation,
    but less accurate results.
 
    [Q,FCNT] = QUADL(...) returns the number of function evaluations.
 
    QUADL(FUN,A,B,TOL,TRACE) with non-zero TRACE shows the values
    of [fcnt a b-a Q] during the recursion.
 
    QUADL(FUN,A,B,TOL,TRACE,P1,P2,...) provides for additional 
    arguments P1, P2, ... to be passed directly to function FUN,
    FUN(X,P1,P2,...).  Pass empty matrices for TOL or TRACE to
    use the default values.
 
    Use array operators .*, ./ and .^ in the definition of FUN
    so that it can be evaluated with a vector argument.
 
    Function QUAD may be more efficient with low accuracies or
    nonsmooth integrands.
 
    Example:
        FUN can be specified three different ways.
 
        A string expression involving a single variable:
           Q = quadl('1./(x.^3-2*x-5)',0,2);
 

        An inline object:
           F = inline('1./(x.^3-2*x-5)');
           Q = quadl(F,0,2);
 
        A function handle:
           Q = quadl(@myfun,0,2);
           where myfun.m is an M-file:
              function y = myfun(x)
              y = 1./(x.^3-2*x-5);

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