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. تفاصيل المقالة

This paper uses a new framework for solving a class of linear matrix differential equations. For doing so, the operational matrix of the derivative based on the shifted Bernstein polynomials together with the collocation method are exploited to decrease the principal problem to system of linear matrix equations. An error estimation of this method is provided. Numerical experiments are reported to show the applicably and efficiency of the propounded method. تفاصيل المقالة

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 numerical examples. تفاصيل المقالة

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 accurate approximations in many‎ ‎cases in which the collocation method is ‎failed. تفاصيل المقالة

In The current paper presents an idea for solving a class of linear matrix differential equations of second order. To perform so, the operational matrix of the integration based on the Bernstein multi-scaling polynomials are used to reduce the main problem to system of matrix equations. Numerical experiments illustrate the applicably and efficiency of the propounded ‎technique.‎ تفاصيل المقالة

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 provides more accurate and numerically stable solutions. تفاصيل المقالة

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. تفاصيل المقالة

In this research work, we have shown that it is possible to use fuzzy transform method (FTM) for approximate solution of space-time fractional advection-dispersion equation. In numerical methods, in order to approximate a function on a particular interval, only a restricted number of points are employed. However, what makes the F-transform preferable to other methods is that it makes use of all points in the interval. تفاصيل المقالة

In this paper, we propose direct methods to solve linear delay differential equations (DDEs) based on vector forms of Block-Pulse Functions (BPFs) and Triangular Functions (TFs). Operational matrix of integration of BPFs and TFs are applied to transform LDDE to a linear system of algebraic equations. Further, some numerical examples are presented to indicate the reliability and accuracy of these methods. Convergence analysis of the present method has been discussed. تفاصيل المقالة

In this article, a fast numerical approach is proposed for finding the solution of nonlinear delay differential equations by using hybrid Taylor and Block-pulse Functions (HTBPFs). Firstly, some features of hybrid functions which are a combination of Block-Pulse functions and Taylor polynomials on the interval are introduced [0, 1) . In this spectral approach, the operational matrices of stretch, derivation and coefficient matrices are utilized. Based on these piecewise functions, we transfer delay differential equations (DDEs) into a system of linear or nonlinear algebraic equations. Also, in this numerical approach, it is shown that these operational matrices are sparse which is an effective advantage of the fast implementation of numerical computation. Then, error analysis is done. Finally, three examples are solved to show that the new proposed approach is comparable with other methods of high accuracy and efficiency. تفاصيل المقالة