Showing 2 results for Rationalized Haar
Yadollah Ordokhani, Neda Rahimi,
Volume 14, Issue 3 (10-2014)
Abstract
In this paper rationalized Haar (RH) functions method is applied to approximate the numerical solution of the fractional Volterra integro-differential equations (FVIDEs). The fractional derivatives are described in Caputo sense. The properties of RH functions are presented, and the operational matrix of the fractional integration together with the product operational matrix are used to reduce the computation of FVIDEs into a system of algebraic equations. By using this technique for solving FVIDEs time and computational are small. Numerical examples are given to demonstrate application of the presented method with RH functions base.In this paper rationalized Haar (RH) functions method is applied to approximate the numerical solution of the fractional Volterra integro-differential equations (FVIDEs). The fractional derivatives are described in Caputo sense. The properties of RH functions are presented, and the operational matrix of the fractional integration together with the product operational matrix are used to reduce the computation of FVIDEs into a system of algebraic equations. By using this technique for solving FVIDEs time and computational are small. Numerical examples are given to demonstrate application of the presented method with RH functions base.
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.
