QA605 : Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2021
Authors:
Abstarct: One of the most basic problems of numerical analysis is solving integral equations and differential-integral equations. Many important mathematical and physical problems are transformed into integral equations after modeling. Therefore, we are always looking for ways to solve such equations.
One of these methods for solving nonlinear volterra integral equations and quadrati linear Volterra integral-differential equations presented in this thesis is Legender-collocation method. In this method using a few changing preliminary variables. We transform it into the suitable equation so that we can use the Gauss-Legender formula and obtain an approximation for these equations using Lagrange interpolation polynomials. In the following, we will deal with the main theorem that plays an essential role in convergence analysis and provide a very accurate error analysis for the proposed method L_∞-norm and L_2-norm.
Finally, by solving a few numerical examples, we show that the numerical errors in L_∞-norm and L_2-norm are reduced exponentiall.
Keywords:
#Integral equations #Legendre-collocation methods #Volterra integral equation #convergence analysis. Keeping place: Central Library of Shahrood University
Visitor:
Visitor:
