In this paper, we present a method to solve nonlinear Volterra-Fredholm-Hammerestein integral equations in terms of LEGENDRE POLYNOMIALs. Properties of these POLYNOMIALs and operational matrix of integration together with the product operational matrix are first presented. These properties are then utilized to transform the integral equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown LEGENDRE coefficients. Finally, numerical examples illustrate the efficiency and accuracy of the method.

In this paper, interval LEGENDRE wavelet method is investigated to approximated the solution of the interval Volterra-Fredholm-Hammerstein integral equation. The shifted interval LEGENDRE POLYNOMIALs are introduced and based on interval LEGENDRE wavelet method is de ned. The existence and uniqueness theorem for the interval Volterra-Fredholm-Hammerstein integral equations is proved. Some examples show the e ectiveness and e ciency of the approach.

Variace / covariance components of 227118 first lactaiom test-day milk yield records belonged to 31258 Iranian Holstein cows were estimated using nine random regression models. Afterwards, different measures of persistency based on estimation breeding value were evaluated. Three functions were used to adjust fixed lactation curve: Ali and Schaeffer (AS), quadratic (LE3) and cubic (LE4) order of LEGENDRE POLYNOMIAL but for random effects, unequal order of LEGENDRE POLYNOMIALs (LE3, LE4, LE5 and Ali and Schaffer) functions were evaluated. Heterogeneous residual variance considered during days in milk and evaluation of models was based on eigenvalues and associated eigenvectors and residual variance. Model with Ali and Schaeffer function for fixed part and LE3 and LE4 for additive and permanent environmental effects was selected as the best model for random regression analysis in first parity dairy cows. The highest and lowest heritability were observed in the middle (0.29) and beginning (0.08) of lactation, respectively. Persistency measurement proposed by Cobuci (PSY1) (difference between estimation breeding value between 290 and 90 days) was preferential for using in further genetic evaluations for persistency in milk yield of Iranian Holstein cows.

In this paper we propose a method for computing approximations of solution of fractional differential equations using LEGENDRE POLYNOMIALs and Adomian decomposition method.

In this paper, we develop a framework to obtain approximate numerical solutions to ordinary differential equations (ODEs) involving fractional order derivatives using LEGENDRE wavelets approximations. The continues LEGENDRE wavelets constructed on [0,1] are utilized as a basis in collocation method. Illustrative examples are included to demonstrate the validity and applicability of the technique.