In this paper, we use a combination of Legendre and Block-Pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.The nonlinear part of the integral equation is approximated by Hybrid Legen-dre Block-Pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. We give some numerical examples. To showapplicability of...

A method for finding the solution of a linear time varying multidelay systems using a hybrid function is proposed. The properties of the hybrid functions which consists of block-pulse functions plus Legendre polynomials are presented. The method is based upon expanding various time functions in the system as their truncated hybrid functions. Operational matrices of integration, delay and produc...

A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equ...

In this paper a hybrid algorithm based on exploration power of the Genetic algorithms and exploitation capability of Nelder Mead simplex is presented for global optimization of multi-variable functions. Some modifications are imposed on genetic algorithm to improve its capability and efficiency while being hybridized with Simplex method. Benchmark test examples of structural optimization with a...

let $x$ be a reflexive banach space, $t:xto x$ be a nonexpansive mapping with $c=fix(t)neqemptyset$ and $f:xto x$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. in this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences t...

Traditionally, the three important manufacturing functions, which are process planning, scheduling and due-date assignment, are performed separately and sequentially. For couple of decades, hundreds of studies are done on integrated process planning and scheduling problems and numerous researches are performed on scheduling with due date assignment problem, but unfortunately the integration of ...

Pfaffian Hybrid Systems. Pfaffian hybrid systems, which we recently introduced in [18], are a sub-class of o-minimal hybrid systems which capture rich continuous dynamics and yet can be studied using finite bisimulations. In particular Pfaffian hybrid systems include hybrid systems with continuous dynamics definable by functions such as exp, sin, cos, and other trigonometric functions in approp...

Properties of the hybrid of block-pulse functions and Lagrange polynomials based on the Legendre-Gauss-type points are investigated and utilized to define the composite interpolation operator as an extension of the well-known Legendre interpolation operator. The uniqueness and interpolating properties are discussed and the corresponding differentiation matrix is also introduced. The appl...

A numerical method for solving nonlinear mixed Hammerstein integral equations is presented in this paper. The method is based upon hybrid of rationalized Haar functions approximations. The properties of hybrid functions which are the combinations of block-pulse functions and rationalized Haar functions are first presented. The Newton-Cotes nodes and Newton-Cotes integration method are then util...