Parallel interval Newton-like Schwarz methods for almost linear parabolic problems (Q861926)

This paper deals with parallel interval Newton-Schwarz-like methods for systems of nonlinear algebraic equations arising from discretizations of almost linear parabolic problems of the type \[ u_t - Lu + \phi(u) = 0, \quad \Omega\times [0,T], \quad \Omega \subset \mathbb{R}^m, \quad m = 2,3, \] subject to suitable initial and boundary conditions. By applying interval techniques global convergence properties are obtained, and enclosures are verified. Further, parallelism is introduced by domain decomposition. Numerical results are supplied in supporting the theoretical results.