Optimal solutions for homogeneous and non-homogeneous equations arising in physics

In this study, we present a new modified convergent analytical algorithm for the solution of nonlinear boundary value problems by the Variation of Parameters Method (VPM). The method is based on embedding, auxiliary parameter and auxiliary linear differential operator, provides a computational advantage for the convergence of approximate solutions for nonlinear differential equations. Convergence of developed scheme is also shown and discussed in detail. Moreover, a convenient way is considered for choosing an optimal value of auxiliary parameter via minimizing the residual error over the domain of problem. The accuracy and efficiency of the proposed algorithm is established by implementing on some physical problems. The obtained graphical and numerical results clearly reflects the accuracy and convergence of the presented algorithm.