【摘要】 基于文献[1]给出了一种数值证明变分不等式解的存在性方法。通过Hilbert空间中的Riesz表示定理,首先将变分不等式问题的迭代过程转化为一种不动点形式,再利用Schauder不动点定理构造了一个高效率的数值证明过程,即通过数值计算产生一个包含近似解的有界闭凸子集。非线性Helmholtz方程的算例说明这一方法的可行性和高效性。更多还原

【Abstract】 In this paper,a numerical method to verify the existence of solutions for variational inequalities is presented.This method is based on the work of reference([1]).By using the Riesz present theory in Hilbert space,we first transform the iterative procedure of variational inequalities into a fixed point form.Then,using the Schauder fixed point theory,we construct a numerical verification method with high efficiency that through numerical computation generates a bounded,closed,convex set in which the approximate solution is included.Finally,a numerical example for nonlinear Helmholtz equation is presented.更多还原