Variation of Parameters Method for Initial and Boundary Value Problems

In this paper, we apply the Variation of Parameters Method (VPM) for solving initial and boundary value problems of diversified physical nature. The analytical results are calculated in terms of convergent series with easily computable components. The proposed VPM is applied without any discretization, perturbation, transformation or restrictive assumptions and is free from round off errors and calculation of the so-called Adomian’s polynomials. The suggested algorithm is tested on higher dimensional initial and boundary value problems, Boussinesq and Helmholtz equations and nonlinear boundary value problems of various orders. Numerical results reveal the complete reliability of the proposed VPM.