  In this work, a new technique has been presented to find approximate solution
of linear integro-differential equations. The method is based on modified
orthonormal Bernoulli polynomials and an operational matrix thereof. The method
converts a given integro-differential equation into a set of algebraic
equations with unknown coefficients, which is easily obtained with help of the
known functions appearing in the equation, modified Bernoulli polynomials and
operational matrix. Approximate solution is obtained in form of a polynomial of
required degree. The method is also applied to three well known
integro-differential equations to demonstrated the accuracy and efficacy of the
method. Numerical results of approximate solution are plotted to compared with
available exact solutions. Considerably small error of approximation is
observed through numerical comparison, which is further reducible to a required
level of significance. Method is comparatively simpler and shorter than many
existing methods.
