On the stability of the one-step exact collocation methods for the numerical solution of the second kind Volterra integral equation

1989 ◽  
Vol 29 (2) ◽  
pp. 258-269 ◽  
Author(s):  
M. R. Crisci ◽  
E. Russo ◽  
A. Vecchio
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Volterra Integral Equation ◽  
Collocation Methods ◽  
One Step ◽  
The Stability ◽  
The One

scholarly journals On the Analysis of Numerical Methods for Nonstandard Volterra Integral Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
H. S. Mamba ◽  
M. Khumalo
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation ◽  
Existence And Uniqueness ◽  
Numerical Experiments ◽  
Numerical Solutions ◽  
Trapezoidal Rule ◽  
Collocation Methods ◽  
Point Collocation ◽  
The One ◽  
Theoretical Results

We consider the numerical solutions of a class of nonlinear (nonstandard) Volterra integral equation. We prove the existence and uniqueness of the one point collocation solutions and the solution by the repeated trapezoidal rule for the nonlinear Volterra integral equation. We analyze the convergence of the collocation methods and the repeated trapezoidal rule. Numerical experiments are used to illustrate theoretical results.

scholarly journals On the Stability of Numerical Methods for Nonlinear Volterra Integral Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-18 ◽  
Author(s):  
E. Messina ◽  
Y. Muroya ◽  
E. Russo ◽  
A. Vecchio
Keyword(s):  
Integral Equation ◽  
Numerical Methods ◽  
Numerical Solution ◽  
Volterra Integral Equation ◽  
Linear Part ◽  
Approximate Solutions ◽  
Constant Sign ◽  
Quadrature Methods ◽  
Decay Of Solutions ◽  
The Stability

Here we investigate the behavior of the analytical and numerical solution of a nonlinear second kind Volterra integral equation where the linear part of the kernel has a constant sign and we provide conditions for the boundedness or decay of solutions and approximate solutions obtained by Volterra Runge-Kutta and Direct Quadrature methods.

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