Showing 4 results for Operational Matrix
Volume 9, Issue 1 (10-2010)
Abstract
A direct method to determine numerical solutions of linear Volterra integro-differential equations is presented in this paper.. This method is based on block-pulse functions and its operational matrix. By using this approach, the integro-differential equation reduces to a linear lower triangular system of algebraic equations which can be solved easily. Some numerical examples are provided to illustrate accuracy and computational efficiency of the method. MSC: 45J05 41A30
S Davaeefar, Yadollah Ordokhani,
Volume 13, Issue 2 (7-2013)
Abstract
In this article, the efficient numerical methods for finding solution of the linear and nonlinear Fredholm integral equations of the second kind on base of Bernstein multi scaling functions are being presented. In the beginning the properties of these functions, which are a combination of block-pulse functions on , and Bernstein polynomials with the dual operational matrix are presented. Then these properties are used for the purpose of conversion of the mentioned integral equation to a matrix equation that are compatible to a algebraic equations system. The imperative of the Bernstein multi scaling functions are, for the proper quantitative value of and have a high accuracy and specifically the relative errors of the numerical solutions will be minimum. The presented methods from the standpoint of computation are very simple and attractive and the numerical examples which were presented at the end shows the efficiency and accuracy of these methods.
Volume 18, Issue 44 (10-2009)
Abstract
Hybrid of rationalized Haar functions are developed to approximate the solution of the differential equations. The properties of hybrid functions which are the combinations of block-pulse functions and rationalized Haar functions are first presented. These properties together with the Newton-Cotes nodes are then utilized to reduce the differential equations to the solution of algebraic equations. The method is computationally attractive, and applications are demonstrated through illustrative examples.
Volume 18, Issue 48 (2-2007)
Abstract
A numerical method for solving variational problems is presented in this paper. The method is based upon hybrid of Hartley functions approximations. The properties of hybrid functions which are the combinations of block-pulse functions and Hartley functions are first presented. The operational matrix of integration is then utilized to reduce the variational problems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
