We study the strong convergence of the general one-step method for neutral stochastic delay differential equations with a variable delay.First,we give the notions of C-stability and B-consistency,and then establish a ...We study the strong convergence of the general one-step method for neutral stochastic delay differential equations with a variable delay.First,we give the notions of C-stability and B-consistency,and then establish a fundamental theorem of strong convergence for the general one-step method solving the nonlinear neutral stochastic delay differential equations,where the corresponding diffusion coefficient with respect to the non-delay variables is highly nonlinear.Then,we construct the split-step backward Euler method which is a special implicit one-step method,and prove that it is C-stable,B-consistent,and strongly convergent of order 1/2.Finally,we give some numerical experiments to support the obtained results.展开更多
基金supported by the Key Research Program of Higher Education Institutions of Henan Province(No.24B110019)Basic Research Projects of Key Scientific Research Projects Plan in Henan Higher Education Institutions(No.24ZX008)NSF of China(Nos.12171441 and 12301502).
文摘We study the strong convergence of the general one-step method for neutral stochastic delay differential equations with a variable delay.First,we give the notions of C-stability and B-consistency,and then establish a fundamental theorem of strong convergence for the general one-step method solving the nonlinear neutral stochastic delay differential equations,where the corresponding diffusion coefficient with respect to the non-delay variables is highly nonlinear.Then,we construct the split-step backward Euler method which is a special implicit one-step method,and prove that it is C-stable,B-consistent,and strongly convergent of order 1/2.Finally,we give some numerical experiments to support the obtained results.
