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 79
- Downloads 0
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...
The Impact of Consumption on an Investor’s Strategy under Stochastic Interest Rate and Correlating Brownian Motions
In this work, we consider that an investor’s portfolio comprises of two assets- a risk-free asset driven by Ornstein-Uhlenbeck Stochastic interest rate of return model and the second asset a risky stock with a price proc...
The Condition Numbers of Semi-simple Eigenvalue of Quadratic Eigenvalue Problem
The condition numbers of eigenvalues of matrices measure the sensitivities of eigenvalues to small perturbation of matrix. They're widely used to assess the quality of numerical algorithms for eigenvalue problems. This p...
A Note on the Oscillatory Nature of Lienard Equation
In this paper we consider the problem about the conditions on f(x), g(x) and a(t) to ensure that all solutions of (1) are continuable and oscillatory using non usual assumptions.
Coefficient Bounds for Bazilevic Functions Associated with Modified Sigmoid Function
The focus of the present paper is to obtain the sharp upper bounds of and for functions belonging to the Bazilevic class associated with modified sigmoid function. The connection of these bounds to the celebrated Fek...