Numerical existence and uniqueness proof for solutions of nonlinear hyperbolic equations
Numerical existence and uniqueness proof for solutions of nonlinear hyperbolic equations
复制标题
非线性双曲方程解的数值存在唯一性证明
DOI：
10.1016/s0377-0427(00)00563-x
复制
发表时间：
1999
影响因子：
2.4
通讯作者：
Teruya Minamoto
中科院分区：
文献类型：
--
作者：
Teruya Minamoto
本文考虑了一种数值方法来证明非线性双曲型问题解的存在唯一性，并给出了保证误差界的条件。利用一个C1有限元解和一个构成线性化算子的逆算子范数的界的不等式，在计算机上构造了一组满足Lp-空间上连续映射的Banach不动点定理假设的函数.我们提出了详细的验证程序，并给出了一些数值例子。
We consider a numerical method to verify the existence and uniqueness of the solutions of nonlinear hyperbolic problems with guaranteed error bounds. Using a C1finite element solution and an inequality constituting a bound on the norm of the inverse operator of the linearized operator, we numerically construct a set of functions which satisfy the hypothesis of Banach's fixed point theorem for a continuous map on Lp-space in a computer. We present detailed verification procedures and give some numerical examples.