  A new technique is presented to solve a class of linear boundary value
problems (BVP). Technique is primarily based on an operational matrix developed
from a set of modified Bernoulli polynomials. The new set of polynomials is an
orthonormal set obtained with Gram-Schmidt orthogonalization applied to
classical Bernoulli polynomials. The presented method changes a given linear
BVP into a system of algebraic equations which is solved to find an approximate
solution of BVP in form of a polynomial of required degree. The technique is
applied to four problems and obtained approximate solutions are graphically
compared to available exact and other numerical solutions. The method is
simpler than many existing methods and provides a high degree of accuracy.
