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Methods of Numerical Integration

Solving a nonlinear fractional differential equation using Chebyshev wavelets

The Riemann-Liouville fractional integral for repeated fractional integration is expanded in block pulse functions to yield the block pulse operational matrices for the fractional order integration. Also, the generalized block pulse operational matrices of differentiation are derived. Based on the above results we propose a way to solve the fractional differential equations. The method is computationally attractive and applications are demonstrated through illustrative examples.

Numerical solution of fractional differential equations using the generalized block pulse operational matrix

An effective direct method to determine the numerical solution of the specific nonlinear Volterra-Fredholm integro-differential equations is proposed. The method is based on new vector forms for representation of triangular functions and its operational matrix. This approach needs no integration, so all calculations can be easily implemented. Some numerical examples are provided to illustrate the accuracy and computational efficiency of the method.

Numerical solution of nonlinear Volterra-Fredholm integro-differential equations via direct method using triangular functions

This paper introduces an approach for obtaining the numerical solution of the nonlinear Volterra-Fredholm integro-differential (NVFID) equations using hybrid Legendre polynomials and Block-Pulse functions. These hybrid functions and their operational matrices are used for representing matrix form of these equations. The main characteristic of this approach is that it reduces NVFID equations to a system of algebraic equations, which greatly simplifying the problem. Numerical examples illustrate the validity and applicability of the proposed method.

Hybrid Legendre polynomials and Block-Pulse functions approach for nonlinear Volterra-Fredholm integro-differential equations

Direct method to solve Volterra integral equation of the first kind using operational matrix with block-pulse functions

In this paper a moment method simulation of electromag- netic scattering problem is presented. An effective numerical method for solving this problem based on the method of moments and using block-pulse basis functions is proposed. Some examples of engineer- ing interest are included to illustrate the procedure. The scattering problem is treated in detail, and illustrative computations are given for some cases. This method can be generalized to apply to objects of arbitrary geometry and arbitrary material.

/pdf/a-moment-method-simulation-of-electromagnetic-scattering-29ydr9hx5v.pdf

A moment method simulation of electromagnetic scattering from conducting bodies

A new and effective direct method to determine the numerical solution of specific nonlinear Volterra-Fredholm integral and integro-differential equations is proposed. The method is based on vector forms of block-pulse functions (BPFs). By using BPFs and its operational matrix of integration, an integral or integro-differential equation can be transformed to a nonlinear system of algebraic equations. Some numerical examples are provided to illustrate accuracy and computational efficiency of the method. Finally, the error evaluation of this method is presented. The benefits of this method are low cost of setting up the equations without applying any projection method such as Galerkin, collocation, . . . . Also, the nonlinear system of algebraic equations is sparse. 60 Babolian, Masouri, and Hatamzadeh-Varmazyar

/pdf/new-direct-method-to-solve-nonlinear-volterra-fredholm-fq9yk5dseg.pdf

New direct method to solve nonlinear volterra-fredholm integral and integro-differential equations using operational matrix with block-pulse functions

E. Babolian a, Z. Masouri b , S. Hatamzadeh-Varmazyar c (a) Department of Mathematics, Teacher Training University, Tehran, Iran (b) Department of Mathematics, Khorramabad Branch, Islamic Azad University, Khorramabad, Iran (c) Department of Electrical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran |||||||||||||||||||||||||||||||Abstract A practical direct method to compute numerical solutions of the linear Volterra and Fredholm integral equations system is proposed. This approach is based on vector forms of triangular functions and its operational matrices and without any integration reduces an integral equations system to a system of algebraic equations. Numerical results of some examples show that the method is practical and has high accuracy.

https://ijim.srbiau.ac.ir/article_2018_4c7a85b99689a4b31008d117da60348d.pdf

Zahra Masouri

Papers

Direct method to solve Volterra integral equation of the first kind using operational matrix with block-pulse functions

Numerical solution of nonlinear Volterra-Fredholm integro-differential equations via direct method using triangular functions

A moment method simulation of electromagnetic scattering from conducting bodies

New direct method to solve nonlinear volterra-fredholm integral and integro-differential equations using operational matrix with block-pulse functions

A Direct Method for Numerically Solving Integral Equations System Using Orthogonal Triangular Functions