We investigate a class of ecological models with local-nonlocal diffusions and different free boundaries.This is PartⅠof a two-part series,in which the existence,uniqueness,regularity and estimates of global solution...We investigate a class of ecological models with local-nonlocal diffusions and different free boundaries.This is PartⅠof a two-part series,in which the existence,uniqueness,regularity and estimates of global solution is studied.The spreading-vanishing dichotomy,criteria governing spreading and vanishing,long-time behavior of solution and the estimation of the spreading speed when spreading happens will be studied in the separate PartⅡ.展开更多
In this paper well-conditioning of boundary value problems for systems of second order difference equa-tions is studied.First,a sufficient condition for the existence of a unique bounded solution (for large enough num...In this paper well-conditioning of boundary value problems for systems of second order difference equa-tions is studied.First,a sufficient condition for the existence of a unique bounded solution (for large enough number of steps) of an associated homogeneous system is given.Finally,a sufficient condition for well-condi-tioning,intrinsically related to the problem data is proposed.展开更多
A numerical method based on finite difference method with variable mesh is given for self-adjoint singularly perturbed two-point boundary value problems. To obtain parameter- uniform convergence, a variable mesh is co...A numerical method based on finite difference method with variable mesh is given for self-adjoint singularly perturbed two-point boundary value problems. To obtain parameter- uniform convergence, a variable mesh is constructed, which is dense in the boundary layer region and coarse in the outer region. The uniform convergence analysis of the method is discussed. The original problem is reduced to its normal form and the reduced problem is solved by finite difference method taking variable mesh. To support the efficiency of the method, several numerical examples have been considered.展开更多
In this paper,the author first establishes the general finite difference formula for the governing equations of the turbulent average velocities in a steady two dimensional incompressible fluid boundary layer-inner la...In this paper,the author first establishes the general finite difference formula for the governing equations of the turbulent average velocities in a steady two dimensional incompressible fluid boundary layer-inner layer.Next, three key parameters of the difference scheme are determined respectively by several simple flow models with known analytical solutions.Finally a special five points difference system is given and its application value is showed by a numerical example for the vertical velocity distribution in an Ekman's layer.展开更多
基金Supported by NSFC Grants(Grant Nos.12171120,11971128)。
文摘We investigate a class of ecological models with local-nonlocal diffusions and different free boundaries.This is PartⅠof a two-part series,in which the existence,uniqueness,regularity and estimates of global solution is studied.The spreading-vanishing dichotomy,criteria governing spreading and vanishing,long-time behavior of solution and the estimation of the spreading speed when spreading happens will be studied in the separate PartⅡ.
基金This work has been partially supported by the "Generalitat Valenciana" grant GV1118/93the Spanish D. G. I. C. Y.T. grant PB93-0381
文摘In this paper well-conditioning of boundary value problems for systems of second order difference equa-tions is studied.First,a sufficient condition for the existence of a unique bounded solution (for large enough number of steps) of an associated homogeneous system is given.Finally,a sufficient condition for well-condi-tioning,intrinsically related to the problem data is proposed.
文摘A numerical method based on finite difference method with variable mesh is given for self-adjoint singularly perturbed two-point boundary value problems. To obtain parameter- uniform convergence, a variable mesh is constructed, which is dense in the boundary layer region and coarse in the outer region. The uniform convergence analysis of the method is discussed. The original problem is reduced to its normal form and the reduced problem is solved by finite difference method taking variable mesh. To support the efficiency of the method, several numerical examples have been considered.
文摘In this paper,the author first establishes the general finite difference formula for the governing equations of the turbulent average velocities in a steady two dimensional incompressible fluid boundary layer-inner layer.Next, three key parameters of the difference scheme are determined respectively by several simple flow models with known analytical solutions.Finally a special five points difference system is given and its application value is showed by a numerical example for the vertical velocity distribution in an Ekman's layer.
