  Study of scattering process in the nonlocal interaction framework leads to an
integro-differential equation. The purpose of the present work is to develop an
efficient approach to solve this integro-differential equation with high degree
of precision. The method developed here employs Taylor approximation for the
radial wave function which converts the integro-differential equation in to a
readily solvable second-order homogeneous differential equation. This scheme is
found to be computationally efficient by a factor of 10 when compared to the
iterative scheme developed in J.~Phys.~G~Nucl.~Part.~Phys.~{\bf
45},~015106~(2018). The calculated observables for neutron scattering off
$^{24}$Mg, $^{40}$Ca, $^{100}$Mo and $^{208}$Pb with energies up to 10 MeV are
found to be within at most 8$\%$ of those obtained with the iterative scheme.
Further, we propose an improvement over the Taylor scheme that brings the
observables so close to the results obtained by iterative scheme that they are
visually indistinguishable. This is achieved without any appreciable change in
the run time.
