The Numerical Solution of Singularly Perturbed Nonlinear Partial Differential Equations in Three Space Variables: The Adaptive Explicit Inverse Preconditioning Approach. (2nd January 2019)

• Record Type: Journal Article
• Authors: Lipitakis, Anastasia-Dimitra
• Other Names: Calì Michele Academic Editor.
• Is Part Of: Modelling and simulation in engineering. Volume 2019(2019)
• Publication Date: 2019-01-02
• Subjects: Engineering -- Simulation methods -- Periodicals; Engineering -- Mathematical models -- Periodicals; 620.004
• DOI: 10.1155/2019/5157145
• Languages: English
• ISSNs: 1687-5591

Abstract

Abstract : Critical comments on the complexity of computational systems and the basic singularly perturbed (SP) concepts are given. A class of several complex SP nonlinear elliptic equations arising in various branches of science, technology, and engineering is presented. A classification of complex SP nonlinear PDEs with characteristic boundary value problems is described. A modified explicit preconditioned conjugate gradient method based on explicit inverse preconditioners is presented. The numerical solution of a characteristic 3D SP nonlinear parabolic model is analytically given and numerical results for several model problems are presented demonstrating both applicability and efficiency of the new computational methods.