Numerical methods for the solution of a human capital model

Two finite-difference methods are constructed and used for the solution of a class of endogenous growth model with physical and human capital. Although both the numerical methods to be developed are implicit by construction, each of the methods can be implemented explicitly. The first method is second-order accurate whilst the second is of order one. Because it satisfies a "positivity condition", the first order method will be seen to be unconditionally-convergent to the correct equilibrium solution for all parameter values used in the simulation. On the other hand, the second-order method, obtained by taking a linear combination of first-order schemes, exhibits contrived numerical instabilities for certain choices of parameter values. Other standard methods like the widely-used Runge-Kutta and Euler methods also fail for certain parameter values.