An efficient method for solving nonlocal initial-boundary value problems for linear and nonlinear first-order hyperbolic partial differential equations

• Published in: Journal of applied mathematics & computing Vol. 43; no. 1-2; pp. 31 - 54
• Main Author: Bougoffa, Lazhar
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2013; Springer Nature B.V
• Subjects: Applied mathematics; Boundary conditions; Boundary value problems; Computational Mathematics and Numerical Analysis; Computer science; Decomposition; Hilbert space; Initial value problems; Linear equations; Mathematical analysis; Mathematical and Computational Engineering; Mathematics; Mathematics and Statistics; Mathematics of Computing; Nonlinearity; Original Research; Partial differential equations; Polynomials; Studies; Theory of Computation; Transforms; 35K20; Adomian polynomials; Adomian decomposition method; 34B10; 35L15; Systems of first-order hyperbolic partial differential equations; Nonlocal initial-boundary value problem; 35K55; First-order hyperbolic partial differential equations; 35L20
• ISSN: 1598-5865; 1865-2085
• DOI: 10.1007/s12190-013-0650-8

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.