On the Regularization-Homotopy Analysis Method for Linear and Nonlinear Fredholm Integral Equations of the First Kind
Journal Title: Asian Research Journal of Mathematics - Year 2017, Vol 4, Issue 1
Abstract
Fredholm integral equations of the first kind are considered by applying regularization method and the homotopy analysis method. This kind of integral equations are considered as an ill-posed problem and for this reason needs an effective method in solving them. This method first transforms a given Fredholm integral equation of the first kind to the second kind by the regularization method and then solves the transformed equation using homotopy analysis method. Approximation of the solution will be of much concern since it is not always the case to get the solution to converge and the existence of the solution is not always guaranteed as this kind of Fredholm integral equation is not well-posed.
Authors and Affiliations
Ibrahim Issaka, William Obeng-Denteh, Isaac Owusu Mensah, Edward Prempeh, Patrick Akwasi Anamuah Mensah
Keywords
Related Articles
- EP ID EP338406
- DOI 10.9734/ARJOM/2017/32585
- Views 85
- Downloads 0
Limit and Continuity Revisited via Convergence
We derive some of the standard results on limits of elementary functions de ned on subsets of real-line, whose rigorous proofs are often avoided in the routine teaching and learning of calculus. For proofs, we essentiall...
Peristaltic Transport with Viscous Dissipation Effect in a Multi-stenosed Artery
In this paper, we investigated the effect of pulse amplitude, radius of constriction and Reynolds number on the blood flow through a multi-stenosed artery under the influence of viscous dissipation and insignificant free...
On Non-existence of Global Weak-predictable-random-field Solutions to a Class of SHEs
The multiplicative non-linearity term is usually assumed to be globally Lipschitz in most results on SPDEs. This work proves that the solutions fail to exist if the non-linearity term grows faster than linear growth. The...
Investor’s Power Utility Optimization with Consumption, Tax, Dividend and Transaction Cost under Constant Elasticity of Variance Model
This work considered an investor’s portfolio where consumption, taxes, transaction costs and dividends are in involved, under constant elasticity of variance (CEV). The stock price is assumed to be governed by a constant...
Degree-correlation, Robustness and Vulnerability in Finite Scale-free Networks
Many naturally occurring networks have a power-law degree distribution as well as a non-zero degree correlation. Despite this, most studies analyzing the robustness to random node- deletion and vulnerability to targeted...