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PIER PIER B PIER C PIER M PIER Letters PIER Photonics
2008-05-30
New Direct Method to Solve Nonlinear Volterra-Fredholm Integral and Integro-Differential Equations Using Operational Matrix with Block-Pulse Functions
By
Esmail Babolian,

    Professor Esmail Babolian

    Department of Electrical Engineering

    Islamic Azad University

    Iran

    Homepage

Zahra Masouri,

    Dr. Zahra Masouri

    Department of Mathematics

    Islamic Azad University

    Iran

    Homepage

Saeed Hatamzadeh

    Dr. Saeed Hatamzadeh

    Department of Electrical Engineering

    Science and Research Branch, Islamic Azad University

    Iran

    Homepage

Progress In Electromagnetics Research B, Vol. 8, 59-76, 2008
doi:10.2528/PIERB08050505 | Google Scholar

Abstract
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.
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Citation
Esmail Babolian, Zahra Masouri, and Saeed Hatamzadeh, "New Direct Method to Solve Nonlinear Volterra-Fredholm Integral and Integro-Differential Equations Using Operational Matrix with Block-Pulse Functions," Progress In Electromagnetics Research B, Vol. 8, 59-76, 2008.
doi:10.2528/PIERB08050505
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