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No abstract

The present study deals with the numerical solution of the G-heat equation. Since the G-heat equation is defined in an unbounded domain, we firstly state that the solution of the G-heat equation defined in a bounded domain converges to the solution of the G-heat equation when the measure of the domain tends to infinity. Moreover, after time discretisation by an implicit time marching scheme, we define a method of linearisation of each stationary problem, which leads to the solution of a large scale algebraic system. A unified approach analysis of the convergence of the sequential and parallel relaxation methods is given. Finally, we present the results of numerical experiments. . He teaches numerical analysis, optimisation and numerical solution of boundary value problems. His fields of interest are in numerical analysis, large scale nonlinear systems of evolution equations, optimal control, parallel computing and more particularly, domain decomposition methods for the solution of nonlinear boundary values problems; he is interested to apply the obtained theoretical results to applications concerning finance, image processing, mechanics, etc. He is also a scientific expert, advisor and referee for several international scientific committees and journals.

No abstract

The present study deals with the numerical solution of the G-heat equation. Since the G-heat equation is defined in an unbounded domain, we firstly state that the solution of the G-heat equation defined in a bounded domain converges to the solution of the G-heat equation when the measure of the domain tends to infinity. Moreover, after time discretisation by an implicit time marching scheme, we define a method of linearisation of each stationary problem, which leads to the solution of a large scale algebraic system. A unified approach analysis of the convergence of the sequential and parallel relaxation methods is given. Finally, we present the results of numerical experiments.