Preprint no.: 4 2010A CAS Wavelet Method for Solving Nonlinear Fredholm Integro- Differential Equations of Fractional Order

In this paper we present a computational method for solving a class of nonlinear Fredholm integro- differential equations of fractional order which is based on CAS (Cosine And Sine) wavelets. The CAS wavelet operational matrix of fractional integration is derived and used to transform the equation to a system of algebraic equations. some examples are included to demonstrate the validity and applicability of the technique

An operational Haar wavelet method for solving fractional Volterra integral equations

A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the validity and applicability of the developed method

A new hybrid simulated annealing-based genetic programming technique to predict the ultimate bearing capacity of piles

The aim of this research is to develop three soft-computing techniques, including adaptive-neuro-fuzzy inference system (ANFIS), genetic-programming (GP) tree-based, and simulated annealing–GP or SA–GP for prediction of the ultimate-bearing capacity (Qult) of the pile. The collected database consists of 50 driven piles properties with pile length, pile cross-sectional area, hammer weight, pile set and drop height as model inputs and Qult as model output. Many GP and SA–GP models were constructed for estimating pile bearing capacity and the best models were selected using some performance indices. For comparison purposes, the ANFIS model was also applied to predict Qult of the pile. It was observed that the developed models are able to provide higher prediction performance in the design of Qult of the pile. Concerning the coefficient of correlation, and mean square error, the SA–GP model had the best values for both training and testing data sets, followed by the GP and ANFIS models, respectively. It implies that the neural-based predictive machine learning techniques like ANFIS are not as powerful as evolutionary predictive machine learning techniques like GP and SA–GP in estimating the ultimate-bearing capacity of the pile. Besides, GP and SA–GP can propose a formula for Qult prediction which is a privilege of these models over the ANFIS predictive model. The sensitivity analysis also showed that the Qult of pile looks to be more affected by pile cross-sectional area and pile set