The Approximate Solution of Linear Differential Equations

1 I N A recent paper the approximate solution of linear differential equations by a wave perturbation method was described. When the method was applied to equations whose exact solutions were known we were greatly impressed by the rapidity of convergence of the successive approximations. Hence the purpose of this note is to present some illustrations in the hope that others may be interested and may find the proposed method an improvement on those now in use. In essence the wave perturbation method dates back to Liouville 2 , but in his memoires he was interested in a problem of heat conduction involving a non-homogeneous differential equation with homogeneous boundary conditions, whereas we consider a homogeneous equation /' = F{x)y with non-homogeneous initial conditions (2a) (1)