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

Authors

  • 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

Keywords:

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

Abstract

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.

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Published

2018-05-19

Issue

2018: INFORMATION TECHNOLOGIES AND COMPUTER MODELLING proceedings of the International Scientific Conference

Section

Section 8 Applied methods for continuous and discrete mathematical models research