周期摄动守恒系统的数值解

On Numerical Solutios of Periodically Perturbed Conservative Systems

1.
Department of Basic Science, Nanjing University of Chemical Technology, Nanjing 210009, P R China;
2.
Department of Mathematics, Nanjing University, Nanjing 210093, P R China

摘要: 讨论了周期摄动非线性守恒系统。利用Hadamard定理证明了在适当的条件下连续问题解的存在唯一性。并在均匀网格上对方程作了离散化,给出了相应的离散问题具有唯一解的结果。最后讨论了数值解的精度及有关算法。
- 非线性系统 /
- 解的存在唯一性 /
- 数值解 /
- 算法
Abstract: A nonlinear perturbed conservative system is discussed. By means of Hadamard. stheorem, the existence and uniqueness of the solution of the continuous problem are proved. When the equation is discreted on the uniform meshes, it is proved that the corresponding discrete problem has a unique solution. Finally, the accuracy of the numerical solution is considered and a simple algorithm is provided for solving the nonlinear difference equation.
- nonlinear system /
- numerical solution /
- uniqueness and existence /
- algorithm

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