An efficient method for solving nonlocal initial-boundary value problems for linear and nonlinear first-order hyperbolic partial differential equations
In this paper, we present a new approach to solve nonlocal initial-boundary value problems of linear and nonlinear hyperbolic partial differential equations of first-order subject to initial and nonlocal boundary conditions of integral type. We first transform the given nonlocal initial-boundary value problems into local initial-boundary value problems. Then we apply a modified Adomian decomposition method, which permits convenient resolution of these problems. Moreover, we prove this decomposition scheme applied to such nonlocal problems is convergent in a suitable Hilbert space, and then extend our discussion to include systems of first-order linear equations and other related nonlocal initial-boundary value problems.
nonlocal initial-boundary value problem first-order hyperbolic partial differential equations adomian decomposition method systems of first-order hyperbolic partial differential equations adomian polynomials 34b10 35k20 35k55 35l15 35l20