Esmail Babolian
Department of Computer Science, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
[ 1 ] - Fractional-order Legendre wavelets and their applications for solving fractional-order differential equations with initial/boundary conditions
In this manuscript a new method is introduced for solving fractional differential equations. The fractional derivative is described in the Caputo sense. The main idea is to use fractional-order Legendre wavelets and operational matrix of fractional-order integration. First the fractional-order Legendre wavelets (FLWs) are presented. Then a family of piecewise functions is proposed, based on whi...
[ 2 ] - An efficient approximate method for solution of the heat equation using Laguerre-Gaussians radial functions
In the present paper, a numerical method is considered for solving one-dimensional heat equation subject to both Neumann and Dirichlet initial boundary conditions. This method is a combination of collocation method and radial basis functions (RBFs). The operational matrix of derivative for Laguerre-Gaussians (LG) radial basis functions is used to reduce the problem to a set of algebraic equatio...
[ 3 ] - Numerical Study of Unsteady Flow of Gas Through a Porous Medium By Means of Chebyshev Pseudo-Spectral Method
In this work, we first reformulate the unsteady flow of gas through a porous medium problem in [0,+∞) to a problem in [-1,1] by variable transformation μ = (x-s)/(x+s), and using spectral collocation method based on Chebyshev polynomials to approximate the resulting problem. The comparison of the results obtained by this method with results obtained by other methods shows that this method provi...
[ 4 ] - A solution for Volterra Integral Equations of the First Kind Based on Bernstein Polynomials
In this paper, we present a new computational method to solve Volterra integral equations of the first kind based on Bernstein polynomials. In this method, using operational matrices turn the integral equation into a system of equations. The computed operational matrices are exact and new. The comparisons show this method is acceptable. Moreover, the stability of the proposed method is studied.
[ 5 ] - Application of fractional-order Bernoulli functions for solving fractional Riccati differential equation
In this paper, a new numerical method for solving the fractional Riccati differential equation is presented. The fractional derivatives are described in the Caputo sense. The method is based upon fractional-order Bernoulli functions approximations. First, the fractional-order Bernoulli functions and their properties are presented. Then, an operational matrix of fractional order integration...
[ 6 ] - A numerical scheme for space-time fractional advection-dispersion equation
In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed in...
[ 7 ] - An Effective Numerical Technique for Solving Second Order Linear Two-Point Boundary Value Problems with Deviating Argument
Based on reproducing kernel theory, an effective numerical technique is proposed for solving second order linear two-point boundary value problems with deviating argument. In this method, reproducing kernels with Chebyshev polynomial form are used (C-RKM). The convergence and an error estimation of the method are discussed. The efficiency and the accuracy of the method is demonstrated on some n...
[ 8 ] - Local Annihilation Method and Some Stiff Problems
In this article, a new scheme inspired from collocation method is presented for numerical solution of stiff initial-value problems and Fredholm integral equations of the first kind based on the derivatives of residual function. Then, the error analysis of this method is investigated by presenting an error bound. Numerical comparisons indicate that the presented method yields accur...
[ 9 ] - Pseudo-spectral Matrix and Normalized Grunwald Approximation for Numerical Solution of Time Fractional Fokker-Planck Equation
This paper presents a new numerical method to solve time fractional Fokker-Planck equation. The space dimension is discretized to the Gauss-Lobatto points, then we apply pseudo-spectral successive integration matrix for this dimension. This approach shows that with less number of points, we can approximate the solution with more accuracy. The numerical results of the examples are displayed.
[ 10 ] - A new multi-step ABS model to solve full row rank linear systems
ABS methods are direct iterative methods for solving linear systems of equations, where the i-th iteration satisfies the first i equations. Thus, a system of m equations is solved in at most m ABS iterates. In 2004 and 2007, two-step ABS methods were introduced in at most [((m+1))/2] steps to solve full row rank linear systems of equations. These methods consuming less space, are more compress ...
[ 11 ] - On the WZ Factorization of the Real and Integer Matrices
The textit{QIF} (Quadrant Interlocking Factorization) method of Evans and Hatzopoulos solves linear equation systems using textit{WZ} factorization. The WZ factorization can be faster than the textit{LU} factorization because, it performs the simultaneous evaluation of two columns or two rows. Here, we present a method for computing the real and integer textit{WZ} and textit{ZW} factoriz...
[ 12 ] - A Numerical Method for Solving Stochastic Volterra-Fredholm Integral Equation
In this paper, we propose a numerical method based on the generalized hat functions (GHFs) and improved hat functions (IHFs) to find numerical solutions for stochastic Volterra-Fredholm integral equation. To do so, all known and unknown functions are expanded in terms of basic functions and replaced in the original equation. The operational matrices of both basic functions are calculated and em...
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