Numerical solution of linear Fredholm integral equation by using hybrid Taylor and Block-Pulse functions

Numerical solution of Fredholm fuzzy integral equations of the second kind using hybrid of block-pulse functions and Taylor series

“…HBT approach for solving linear Fredholm integral equations has been presented by Maleknejad and Mahmodi [10] and then has been extended by Marzban and Razzaghi to multi-delay systems [9]. Recently, Mirzaee and Hoseini have been used the HBT method to find approximate solutions of nonlinear Volterra and Fredholm integral equations [11].…”

Solution of Multi-Delay Dynamic Systems by Using Hybrid Functions

“…Therefore, it is important to find their approximate solutions by using some numerical methods. In recent years, the hybrid functions consisting of the combination of the Block-Pulse functions with the Chebyshev polynomials [6], the Legendre polynomials [7] [8], or the Taylor series [9] [10] have been shown to be a mathematical power tool for discretization of selected problems. Among these three hybrid functions, hybrids of the BlockPulse functions with the Legendre polynomials have been shown to be computationally more effective.…”

Solving a system of linear Volterra integral equations using the new reproducing kernel method

“…(1) has a unique solution. Volterra integral equation arises in many physical applications, e.g., potential theory and Dirichlet problems, electrostatics, mathematical problems of radiative equilibrium, the particle transport problems of astrophysics and reactor theory and radiative heat transfer problems [1][2][3][4][5]. Several valid methods for solving Volterra integral equations have been developed in recent years, including power series method [6], Adomain's decomposition method [7], homotopy perturbation method [8,9], block by block method [10], expansion method [11] etc.…”