scholarly journals Integral Equations: Theories, Approximations, and Applications

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1402
Author(s):  
Samad Noeiaghdam ◽  
Denis Sidorov
Keyword(s):  
Integral Equations ◽  
Real Life ◽  
Nonlinear Integral Equations ◽  
Life Problems ◽  
Linear And Nonlinear

Linear and nonlinear integral equations of the first and second kinds have many applications in engineering and real life problems [...]

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 APPLICATION OF THE HOMOTOPY ANALYSIS METHOD FOR SOLVING THE SYSTEMS OF LINEAR AND NONLINEAR INTEGRAL EQUATIONS

2016 ◽  
Vol 21 (3) ◽  
pp. 350-370 ◽  
Author(s):  
Rafal Brociek ◽  
Edyta Hetmaniok ◽  
Jaros law Matlak ◽  
Damian Slota
Keyword(s):  
Approximate Solution ◽  
Integral Equations ◽  
Homotopy Analysis Method ◽  
System Of Equations ◽  
Analysis Method ◽  
Nonlinear Integral Equations ◽  
Function Series ◽  
Partial Sum ◽  
Homotopy Analysis ◽  
Linear And Nonlinear

In this paper we indicate some applications of homotopy analysis method for solving the systems of linear and nonlinear integral equations. The method is based on the concept of creating function series. If the series converges, its sum is the solution of this system of equations. The paper presents conditions to ensure the convergence of this series and estimation of the error of approximate solution obtained when the partial sum of the series is used. Application of the method will be illustrated by examples.

scholarly journals Approximate Solution of Systems of Volterra Integral Equations of Second Kind by Adomian Decomposition Method

2015 ◽  
Vol 63 (1) ◽  
pp. 15-18
Author(s):  
Md Shariful Islam ◽  
Mir Shariful Islam ◽  
Md Zavid Iqbal Bangalee ◽  
AFM Khodadad Khan ◽  
Amal Halder
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Integral Equations ◽  
Decomposition Method ◽  
Real Life ◽  
Adomian Decomposition Method ◽  
Volterra Integral Equations ◽  
Life Problems ◽  
Adomian Decomposition ◽  
Differential And Integral Equations

Real life problems that arise in different branches of science and social science, in the form of differential and integral equations are non-linear in nature. However, methods developed in Mathematics, usually, are suitable for the linear system. In this article, we talk on approximating solution of system of Volterra integral equations of second kind in an analytic way using Adomian decomposition method in Mathematica. DOI: http://dx.doi.org/10.3329/dujs.v63i1.21761 Dhaka Univ. J. Sci. 63(1): 15-18, 2015 (January)

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