通过研究非自治传染病SIRS模型解的存在性和建立迭代算法,分析模型的特殊性质,引入特殊性质的函数,将模型转换为积分系统,并构造所需的迭代序列,证明这个序列收敛于模型的解。可以证明,在一定时间内,SIRS模型具有唯一解,解和近似解之间...通过研究非自治传染病SIRS模型解的存在性和建立迭代算法,分析模型的特殊性质,引入特殊性质的函数,将模型转换为积分系统,并构造所需的迭代序列,证明这个序列收敛于模型的解。可以证明,在一定时间内,SIRS模型具有唯一解,解和近似解之间能进行误差估计。该算法克服模型中非线性项可取负值和不满足Lipschitz条件的困难,证明了SIRS模型解存在,且可使用迭代算法求出和进行误差估计。This paper studies the existence and iterative algorithms of solutions to the SIRS model of non- autonomous infectious diseases. By analyzing the special properties of the model and introducing the function with special properties, the SIRS model is changed to an integral system, and the required iterative sequence is constructed. It is proved that this sequence converges to the solution of the model. It is proved that the SIRS model has a unique solution within a certain period of time, and the error estimations between the exact solution and the approximate solution are established. By overcoming the difficulties that the nonlinear terms in the model may take negative values and do not satisfy the Lipschitz condition, it is proved that the solution of the SIRS model can be obtained by an iterative method, and the error estimation can be performed.展开更多
设 X 是一实的 Banach 空间,T : X → X 是一 Lipschitz 的增生算子。本文证明了具误差 的 Ishikawa 迭代序列强收敛到方程 x + Tx = f 的唯一解;并得一个一般的收敛估计式。 若 T : X → X 是一 Lipschitz 的强增生算子,则具...设 X 是一实的 Banach 空间,T : X → X 是一 Lipschitz 的增生算子。本文证明了具误差 的 Ishikawa 迭代序列强收敛到方程 x + Tx = f 的唯一解;并得一个一般的收敛估计式。 若 T : X → X 是一 Lipschitz 的强增生算子,则具误差的 Ishikawa 迭代序列强收敛到方 程 Tx = f 的唯一解。本文结果推广和发展了现有的相应结果。展开更多
文摘通过研究非自治传染病SIRS模型解的存在性和建立迭代算法,分析模型的特殊性质,引入特殊性质的函数,将模型转换为积分系统,并构造所需的迭代序列,证明这个序列收敛于模型的解。可以证明,在一定时间内,SIRS模型具有唯一解,解和近似解之间能进行误差估计。该算法克服模型中非线性项可取负值和不满足Lipschitz条件的困难,证明了SIRS模型解存在,且可使用迭代算法求出和进行误差估计。This paper studies the existence and iterative algorithms of solutions to the SIRS model of non- autonomous infectious diseases. By analyzing the special properties of the model and introducing the function with special properties, the SIRS model is changed to an integral system, and the required iterative sequence is constructed. It is proved that this sequence converges to the solution of the model. It is proved that the SIRS model has a unique solution within a certain period of time, and the error estimations between the exact solution and the approximate solution are established. By overcoming the difficulties that the nonlinear terms in the model may take negative values and do not satisfy the Lipschitz condition, it is proved that the solution of the SIRS model can be obtained by an iterative method, and the error estimation can be performed.
文摘设 X 是一实的 Banach 空间,T : X → X 是一 Lipschitz 的增生算子。本文证明了具误差 的 Ishikawa 迭代序列强收敛到方程 x + Tx = f 的唯一解;并得一个一般的收敛估计式。 若 T : X → X 是一 Lipschitz 的强增生算子,则具误差的 Ishikawa 迭代序列强收敛到方 程 Tx = f 的唯一解。本文结果推广和发展了现有的相应结果。
