Convergence and stability results in Runge-Kutta type methods for Volterra integral equations of the second kind

1980 ◽  
Vol 20 (3) ◽  
pp. 375-377 ◽  
Author(s):  
P. J. van der Houwen
Keyword(s):  
Integral Equations ◽  
Volterra Integral Equations ◽  
Convergence And Stability ◽  
Runge Kutta ◽  
Stability Results

scholarly journals Convergence and Stability Results of Modified CUIA Iterative Scheme for Hyperbolic Convex Metric space

2021 ◽  
Vol 2089 (1) ◽  
pp. 012040
Author(s):  
Surjeet Singh Chauhan Gonder ◽  
Khushboo Basra
Keyword(s):  
Fixed Points ◽  
Integral Equations ◽  
Metric Space ◽  
Iterative Scheme ◽  
Real Life ◽  
Convex Metric Space ◽  
Convergence And Stability ◽  
Life Problems ◽  
Stability Results ◽  
Differential And Integral Equations

Abstract The iterative fixed points have numerous applications in locating the solution of some real-life problems which can be modelled into linear as well as nonlinear differential and integral equations. In this manuscript, first of all, a new iterative scheme namely Modified CUIA iterative scheme is introduced. We first prove a theorem to check the convergence of this iteration for Hyperbolic Convex metric space. The result is then supported with one example. Further, another theorem is proved establishing the weak T stability of modified CUIA iterative scheme on the above space.

scholarly journals Volterra Runge- Kutta Methods for Solving Nonlinear Volterra Integral Equations

2010 ◽  
Vol 7 (3) ◽  
pp. 1270-1274
Author(s):  
Baghdad Science Journal
Keyword(s):  
Integral Equations ◽  
Volterra Integral Equations ◽  
Least Square ◽  
Runge Kutta

In this paper Volterra Runge-Kutta methods which include: method of order two and four will be applied to general nonlinear Volterra integral equations of the second kind. Moreover we study the convergent of the algorithms of Volterra Runge-Kutta methods. Finally, programs for each method are written in MATLAB language and a comparison between the two types has been made depending on the least square errors.

scholarly journals Runge-Kutta theory for Volterra integral equations of the second kind

1982 ◽  
Vol 39 (159) ◽  
pp. 147-147 ◽  
Author(s):  
H. Brunner ◽  
E. Hairer ◽  
S. P. Nørsett
Keyword(s):  
Integral Equations ◽  
Volterra Integral Equations ◽  
Runge Kutta

A new code for Volterra integral equations based on natural Runge-Kutta methods

2019 ◽  
Vol 143 ◽  
pp. 35-50 ◽  
Author(s):  
A. Abdi ◽  
G. Hojjati ◽  
Z. Jackiewicz ◽  
H. Mahdi
Keyword(s):  
Integral Equations ◽  
Volterra Integral Equations ◽  
Runge Kutta

Highly stable Runge–Kutta methods for Volterra integral equations

2012 ◽  
Vol 62 (8) ◽  
pp. 1002-1013 ◽  
Author(s):  
G. Izzo ◽  
E. Russo ◽  
C. Chiapparelli
Keyword(s):  
Integral Equations ◽  
Volterra Integral Equations ◽  
Runge Kutta

Fast Runge–Kutta methods for nonlinear convolution systems of Volterra integral equations

2007 ◽  
Vol 47 (2) ◽  
pp. 259-275 ◽  
Author(s):  
G. Capobianco ◽  
D. Conte ◽  
I. Del Prete ◽  
E. Russo
Keyword(s):  
Integral Equations ◽  
Volterra Integral Equations ◽  
Runge Kutta ◽  
Convolution Systems
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