Abstract The scalar boundary value problem (BVP) for a nonlinear second order
differential equation on the semiaxis is considered. Under some natural assumptions
it is shown that on an arbitrary finite grid there exists a unique three-point exact
difference scheme (EDS), i.e., a difference scheme whose solution coincides with the
projection of the exact solution of the given differential equation onto the underlying
grid. A constructive method is proposed to derive from the EDS a so-called truncated
difference scheme (n-TDS) of rank n, where n is a freely selectable natural number.
The n-TDS is the basis for a new adaptive algorithm which has
all the advantages known from the modern IVP-solvers. Numerical examples are given
which illustrate the theorems presented in the paper and demonstrate the reliability of
the new algorithm.
Exact solution of the two-axis two-spin Hamiltonian
