Lagrangian Approximations and Collocation Method for Solution of Integral Equations of the First Kind

Olexandr Polishchuk

Lagrangian Approximations and Collocation Method for Solution of Integral Equations of the First Kind

Автор(и)

Olexandr Polishchuk Laboratory of Modeling and Optimization of Complex Systems Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine

Ключові слова:

potential, integral equation, well-posed solvability, Lagrange interpolation, collocation method, convergence

Анотація

This article is dedicated to research of approximation properties of Lagrangian finite elements in Hilbert spaces of functions defined on surfaces in threedimensional space. The conditions are determined for convergence of collocation methods for solving Fredholm integral equation of the first kind for simple layer potential that is equivalent to Dirichlet problem for Laplace equation in R3 . Estimation is determined for the error of approximate solution of this problem obtained using potential theory methods.