In the present paper a numerical method is developed to approximate the solution of two-dimensional Nonlinear Schrodinger equation in the presence of a sin- gular potential. The method leads to generalized Lyapunov-Sy...In the present paper a numerical method is developed to approximate the solution of two-dimensional Nonlinear Schrodinger equation in the presence of a sin- gular potential. The method leads to generalized Lyapunov-Sylvester algebraic opera- tors that are shown to be invertible using original topological and differential calculus issued methods. The numerical scheme is proved to be consistent, convergent and sta- ble using the Lyapunov criterion, lax equivalence theorem and the properties of the generalized Lyapunov-Sylvester operators.展开更多
In this paper a nonlinear Euler-Poisson-Darboux system is considered.In a first part,we proved the genericity of the hypergeometric functions in the development of exact solutions for such a system in some special cas...In this paper a nonlinear Euler-Poisson-Darboux system is considered.In a first part,we proved the genericity of the hypergeometric functions in the development of exact solutions for such a system in some special cases leading to Bessel type differential equations.Next,a finite difference scheme in two-dimensional case has been developed.The continuous system is transformed into an algebraic quasi linear discrete one leading to generalized Lyapunov-Sylvester operators.The discrete algebraic system is proved to be uniquely solvable,stable and convergent based on Lyapunov criterion of stability and Lax-Richtmyer equivalence theorem for the convergence.A numerical example has been provided at the end to illustrate the efficiency of the numerical scheme developed in section 3.The present method is thus proved to be more accurate than existing ones and lead to faster algorithms.展开更多
文摘In the present paper a numerical method is developed to approximate the solution of two-dimensional Nonlinear Schrodinger equation in the presence of a sin- gular potential. The method leads to generalized Lyapunov-Sylvester algebraic opera- tors that are shown to be invertible using original topological and differential calculus issued methods. The numerical scheme is proved to be consistent, convergent and sta- ble using the Lyapunov criterion, lax equivalence theorem and the properties of the generalized Lyapunov-Sylvester operators.
文摘In this paper a nonlinear Euler-Poisson-Darboux system is considered.In a first part,we proved the genericity of the hypergeometric functions in the development of exact solutions for such a system in some special cases leading to Bessel type differential equations.Next,a finite difference scheme in two-dimensional case has been developed.The continuous system is transformed into an algebraic quasi linear discrete one leading to generalized Lyapunov-Sylvester operators.The discrete algebraic system is proved to be uniquely solvable,stable and convergent based on Lyapunov criterion of stability and Lax-Richtmyer equivalence theorem for the convergence.A numerical example has been provided at the end to illustrate the efficiency of the numerical scheme developed in section 3.The present method is thus proved to be more accurate than existing ones and lead to faster algorithms.
