Changing Stopping Criteria for MATLAB ODE113

I am implementing an optimization algorithm which does the following:

1) Evaluates an objective function, its gradient, Hessian, and minimum eigenvalue. 2) Based on the size of the eigenvalue expresses the optimization method as an ODE based on the gradient descent method if the value is small, Newton, or a mix for borderline cases. 3) This ODE is passed to the optimization solver, the answer is taken from the solver, and the function starts again from (1)

The algorithm works to optimizes most of the test problems I have been working on thus far but it doesn't work for 2 and for many of them it doesn't produce similar results to what is reported in the paper.

I double checked the paper and the specifications for ODE113 are:

RelTol = 10^-8

AbsTol = 10^-9

The third option is the one that I am not entirely sure how to implement for ODE113 ( I did check the documentation page). Can someone give me input on how I might changed this to fit the parameters or if it is a default setting?

Additionally, for greater clarity I am providing my code, and how it is implemented/passed to ODE113 below.

if true
  function [ F  ] = zklForODE( func )

     global HoldEigen HoldType;
      HoldType = {0};

       function [dx lambda type] = call_func(t, x)
         [Fx, Gx, Hx,lambda] = feval(func.tional,x);
          sigma1 = 1/(10^9);
        sigma2 =1000*sigma1;
        alph = @(lambda,sig1, sig2) (lambda - sig1)/(sig2 - sig1);

    if lambda > sigma2
        dx = -inv(Hx)*Gx;
        type = 'N';

    elseif lambda < sigma1
        dx = -Gx;
        type = 'G';

    else 
        A = (lambda - sigma1)/(sigma2-sigma1);
        B = 1-A;
        dx = -A*(inv(Hx)*Gx) - B*Gx;
        type = 'M';

      end

        HoldEigen(end+1) = lambda;
        HoldType{end+1} = type;

        disp({Fx, lambda,type  })

     end

      F = @call_func;
     end

 end

The method is then implemented with the following lines:

       global HoldEigen HoldType
      HoldEigen = [0];
     HoldType = {0}

     tic
     func.tional = functional;

     odef = zkl(func);
     options = odeset('RelTol', 1e-8, 'AbsTol', 1e-9, 'NormControl', 'on', 'Stats', 'on');
     [t, answer] = ode113(odef, [0 100], starter',options);
     endans = answer(end,:);
     runtime = toc;

Thanks for your time and attention.