In this paper, the wavelet method based on the Chebyshev polynomials of the second kind is introduced and used to solve systems of integral equations. Operational matrices of integration, product, and derivative are obtained for the second kind Chebyshev wavelets which will be used to convert the system of integral equations into a system of algebraic equations. Also, the error is analyzed and ...

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...

References 1. Bhrawy AH, Taha TM, Alzahrani EO, Baleanu D, Alzahrani AA (2015) New Operational Matrices for Solving Fractional Differential Equations on the Half-Line. PLoS ONE 10(5): e0126620. doi: 10.1371/ journal.pone.0126620 PMID: 25996369 2. Bhrawy AH, Taha TM, Alzahrani EO, Baleanu D, Alzahrani AA (2015) Correction: New Operational Matrices for Solving Fractional Differential Equations on...

An approximation method based on operational matrices of Bernstein polynomials used for the solution of Hammerstein integral equations. The operational matrices of these functions are utilized to reduce a nonlinear Hammerstein and Volterra Hammerstein integral equation to a system of nonlinear algebraic equations. The method is computationally very simple and attractive, and applications are de...

The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which used to solve Falkner-Skan equation. nonlinear differential equation converting a system equations solved using Mathematica®12, approximate solutions are obtained. efficiency these methods was studied by calculating maximum error remainder ( ), it found that their increases as increases. Moreover...

this paper presents an approach for solving a nonlinear stochastic differential equations (nsdes) using a new basis functions (nbfs). these functions and their operational matrices areused for representing matrix form of the nbfs. with using this method in combination with the collocation method, the nsdes are reduced a stochastic nonlinear system of equations and unknowns. then, the error anal...

The exact nonnegative matrix factorization (exact NMF) problem is the following: given an m-by-n nonnegative matrix X and a factorization rank r, find, if possible, an m-by-r nonnegative matrix W and an r-by-n nonnegative matrix H such that X = WH . In this paper, we propose two heuristics for exact NMF, one inspired from simulated annealing and the other from the greedy randomized adaptive sea...