scholarly journals Analysis of Perturbed Volterra Integral Equations on Time Scales

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1133
Author(s):  
Eleonora Messina ◽  
Youssef N. Raffoul ◽  
Antonia Vecchio
Keyword(s):  
Stability Analysis ◽  
Numerical Methods ◽  
Integral Equations ◽  
Time Scales ◽  
Volterra Integral Equations ◽  
Linear Volterra Integral Equations ◽  
New Perspective ◽  
The Stability

This paper describes the effect of perturbation of the kernel on the solutions of linear Volterra integral equations on time scales and proposes a new perspective for the stability analysis of numerical methods.

scholarly journals Stability and Convergence of Solutions to Volterra Integral Equations on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Eleonora Messina ◽  
Antonia Vecchio
Keyword(s):  
Integral Equations ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Volterra Integral Equations ◽  
Stability And Convergence ◽  
Time Behavior ◽  
Convergence Properties ◽  
Convergence Of Solutions ◽  
Long Time ◽  
The Stability

We consider Volterra integral equations on time scales and present our study about the long time behavior of their solutions. We provide sufficient conditions for the stability and investigate the convergence properties when the kernel of the equations vanishes at infinity.

scholarly journals Analytical Solution of System of Volterra Integral Equations Using OHAM

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Muhammad Akbar ◽  
Rashid Nawaz ◽  
Sumbal Ahsan ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Numerical Methods ◽  
Analytical Solution ◽  
Integral Equations ◽  
Function Method ◽  
Auxiliary Function ◽  
Volterra Integral Equations ◽  
Large Parameter ◽  
Reliable Technique ◽  
Present Technique ◽  
Optimal Homotopy Asymptotic Method

In this work, a reliable technique is used for the solution of a system of Volterra integral equations (VIEs), called optimal homotopy asymptotic method (OHAM). The proposed technique is successfully applied for the solution of different problems, and comparison is made with the relaxed Monto Carlo method (RMCM) and hat basis function method (HBFM). The comparisons show that the present technique is more suitable and reliable for the solution of a system of VIEs. The presented technique uses auxiliary function containing auxiliary constants, which control the convergence. Moreover, OHAM does not require discretization like other numerical methods and is also free from small or large parameter.

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