论文标题
涉及内核的积分方程的近似解决方案
Approximate solution of the integral equations involving kernel with additional singularity
论文作者
论文摘要
该论文专用于第二种弗雷德霍尔姆积分方程的近似解决方案，其中弱奇异内核可以在分子中具有额外的奇异性。我们描述了导致这种方程式的两个问题。它们是最小化小偏差和熵最小化问题的问题。当考虑涉及混合分数布朗运动的动态系统时，它们都会出现。为了与内核进行处理，应用众所周知的奇异核的方法，我们证明了对积分方程的溶液近似与内核的近似值的定理，该核包含额外的溶液，其内核的溶液是弱奇异的，但数字是持续的。我们以数值方式证明了我们的方法如何应用于我们的特定积分方程。
The paper is devoted to the approximate solutions of the Fredholm integral equations of the second kind with the weak singular kernel that can have additional singularity in the numerator. We describe two problems that lead to such equations. They are the problem of minimization of small deviation and the entropy minimization problem. Both of them appear when considering dynamical system involving mixed fractional Brownian motion. In order to deal with the kernel with additional singularity applying well-known methods for weakly singular kernels, we prove the theorem on the approximation of solution of integral equation with the kernel containing additional singularity by the solutions of the integral equations whose kernels are weakly singular but the numerator is continuous. We demonstrate numerically how our methods work being applied to our specific integral equations.
