The regularization method is one of the important schemes to solve the ill-posed problems. In this work, by combining the Wazwaz’s regularization method and the homotopy analysis method, a new and robust approach is presented to solve integral equations which is called the homotopy-regularization method. The solution which is produced by the homotopy-regularization method depends on the regularization parameter. In order to find the optimal value of this parameter, the Controle et Estimation Stochastique des Arrondis de Calculs method is applied which is based on the stochastic arithmetic. A theorem is presented to show the accuracy of the proposed approach. Also, in order to implement the algorithm, the Control of Accuracy and Debugging for Numerical Applications library is applied to perform the Controle et Estimation Stochastique des Arrondis de Calculs method in the stochastic arithmetic automatically. Some examples of the singular and ill-posed integral equations are illustrated. The numerical results show the abilities of the Controle et Estimation Stochastique des Arrondis de Calculs method to find the optimal regularization parameter and the optimal approximation of the homotopy-regularization method.
Digital Object Identifier (DOI)
Noeiaghdam, Samad and Ali Fariborzi Araghi, Mohammad
"A Novel Approach to Find Optimal Parameter in the Homotopy-Regularization Method for Solving Integral Equations,"
Applied Mathematics & Information Sciences: Vol. 14
, Article 14.
Available at: https://dc.naturalspublishing.com/amis/vol14/iss1/14