Effect of the Guess Function & Continuation Method on the Run Time of MATLAB BVP Solvers

The MATLAB computing environment is a package used extensively throughout industry, research and education by users of a complete range in proficiency. MATLAB provides then an ideal platform to introduce such an item of Boundary Value Problem (BVP) software and indeed, Kierzenka and Shampine (Kierzenka & Shampine, 2001) developed the core BVP Ordinary Differential Equation (ODE) software bvp4c to solve a large class of two-point boundary value problems of the form