A nonlinear problem of mean-square approximation of a real nonnegative continuous function with respect to two variables by the modulus of double Fourier integral dependent on two real parameters with use of the smoot...A nonlinear problem of mean-square approximation of a real nonnegative continuous function with respect to two variables by the modulus of double Fourier integral dependent on two real parameters with use of the smoothing functional is studied. Finding the optimal solutions of this problem is reduced to solution of the Hammerstein type two-dimensional nonlinear integral equation. The numerical algorithms to find the branching lines and branching-off solutions of this equation are constructed and justified. Numerical examples are presented.展开更多
In this paper, we present a basic theory of mean-square almost periodicity, apply the theory in random differential equation, and obtain mean-square almost periodic solution of some types stochastic differential equat...In this paper, we present a basic theory of mean-square almost periodicity, apply the theory in random differential equation, and obtain mean-square almost periodic solution of some types stochastic differential equation.展开更多
The numerical algorithms for finding the lines of branching and branching-off solutions of nonlinear problem on mean-square approximation of a real finite nonnegative function with respect to two variables by the modu...The numerical algorithms for finding the lines of branching and branching-off solutions of nonlinear problem on mean-square approximation of a real finite nonnegative function with respect to two variables by the modulus of double discrete Fourier transform dependent on two parameters, are constructed and justified.展开更多
The construction of symplectic numerical schemes for stochastic Hamiltonian systems is studied.An approach based on generating functions method is proposed to generate the stochastic symplectic integration of any desi...The construction of symplectic numerical schemes for stochastic Hamiltonian systems is studied.An approach based on generating functions method is proposed to generate the stochastic symplectic integration of any desired order.In general the proposed symplectic schemes are fully implicit,and they become computationally expensive for mean square orders greater than two.However,for stochastic Hamiltonian systems preserving Hamiltonian functions,the high-order symplectic methods have simpler forms than the explicit Taylor expansion schemes.A theoretical analysis of the convergence and numerical simulations are reported for several symplectic integrators.The numerical case studies confirm that the symplectic methods are efficient computational tools for long-term simulations.展开更多
文摘A nonlinear problem of mean-square approximation of a real nonnegative continuous function with respect to two variables by the modulus of double Fourier integral dependent on two real parameters with use of the smoothing functional is studied. Finding the optimal solutions of this problem is reduced to solution of the Hammerstein type two-dimensional nonlinear integral equation. The numerical algorithms to find the branching lines and branching-off solutions of this equation are constructed and justified. Numerical examples are presented.
文摘In this paper, we present a basic theory of mean-square almost periodicity, apply the theory in random differential equation, and obtain mean-square almost periodic solution of some types stochastic differential equation.
文摘The numerical algorithms for finding the lines of branching and branching-off solutions of nonlinear problem on mean-square approximation of a real finite nonnegative function with respect to two variables by the modulus of double discrete Fourier transform dependent on two parameters, are constructed and justified.
文摘The construction of symplectic numerical schemes for stochastic Hamiltonian systems is studied.An approach based on generating functions method is proposed to generate the stochastic symplectic integration of any desired order.In general the proposed symplectic schemes are fully implicit,and they become computationally expensive for mean square orders greater than two.However,for stochastic Hamiltonian systems preserving Hamiltonian functions,the high-order symplectic methods have simpler forms than the explicit Taylor expansion schemes.A theoretical analysis of the convergence and numerical simulations are reported for several symplectic integrators.The numerical case studies confirm that the symplectic methods are efficient computational tools for long-term simulations.
