  A Neural Network (NN) based numerical method is formulated and implemented
for solving Boundary Value Problems (BVPs) and numerical results are presented
to validate this method by solving Laplace equation with Dirichlet boundary
condition and Poisson's equation with mixed boundary conditions. The principal
advantage of NN based numerical method is the discrete data points where the
field is computed, can be unstructured and do not suffer from issues of meshing
like traditional numerical methods such as Finite Difference Time Domain or
Finite Element Method. Numerical investigations are carried out for both
uniform and non-uniform training grid distributions to understand the efficacy
and limitations of this method and to provide qualitative understanding of
various parameters involved.
