Variational iterative method and initial-value problems

Malik Mamode (1)

1 PIMENT - Physique et Ingénierie Mathématique pour l'Énergie, l'environnemeNt et le bâtimenT

The variational iterative method is revisited for initial-value problems in ordinary or partial differential equation. A distributional characterization of the Lagrange multiplier - the keystone of the method - is proposed, that may be interpreted as a retarded Green function. Such a formulation makes possible the simplification of the iteration formula into a Picard iterative scheme, and facilitates the convergence analysis. The approximate analytical solution of a nonlinear Klein-Gordon equation with inhomogeneous initial data is proposed.

Mots clés: Convergence analysis; Green function; Initial-value problem; Nonlinear Klein-Gordon equation; Picard iterative scheme; Variational iterative method

Domaines: Géométrie différentielle [math.DG]

Malik Mamode. Variational iterative method and initial-value problems. Applied Mathematics and Computation, 2009, 215 (1), pp.276--282. ⟨10.1016/j.amc.2009.05.008⟩. ⟨hal-00919547⟩