Volume 7, Issue 1
Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations

Adv. Appl. Math. Mech., 7 (2015), pp. 74-88.

Published online: 2018-03

Preview Full PDF 426 967
Export citation
• Abstract

A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicate that the numerical errors in $L^2$-norm and  $L^\infty$-norm will decay exponentially provided that the kernel function is sufficiently smooth. Numerical results are presented, which confirm the theoretical prediction of the exponential rate of convergence.

• Keywords

A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicate that the numerical errors in $L^2$-norm and  $L^\infty$-norm will decay exponentially provided that the kernel function is sufficiently smooth. Numerical results are presented, which confirm the theoretical prediction of the exponential rate of convergence.