Solving of Linear Volterra-Fredholm Integral Equations via Modification of Block Pulse Functions

Ayyubi Ahmad

doi:10.24198/jmi.v17.n1.32003.33-42

Solving of Linear Volterra-Fredholm Integral Equations via Modification of Block Pulse Functions

Ayyubi Ahmad

Abstract

A computational method based on modification of block pulse functions is proposed for solving numerically the linear Volterra-Fredholm integral equations. We obtain integration operational matrix of modification of block pulse functions on interval [0,T). A modification of block pulse functions and their integration operational matrix can be reduced to a linear upper triangular system. Then, the problem under study is transformed to a system of linear algebraic equations which can be used to obtain an approximate solution of linear Volterra-Fredholm integral equations. Furthermore, the rate of convergence is O(h) and error analysis of the proposed method are investigated. The results show that the approximate solutions have a good of efficiency and accuracy.

Keywords

Brownian Motion, Integration Operational Matrix, Linear Volterra-Fredholm Integral Equations, εMBPFs.

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References

Dastjerdi, H. L. and F. M. Maalek Ghaini. Numerical Solution of Volterra-Fredholm Integral Equations by Moving Least Square Method and Chebyshev Polynomials. Applied Mathematical Modelling, 36(7):3283-3288, 2012.

Hendi, F. A. and A. M. Albugami. Numerical Solution for Fredholm-Volterra Integral Equation of the Second Kind by Using Collocation and Galerkin Methods. Journal of King Saud University (Science), 22(1):37-40, 2010.

Jiang, Z. H. and W. Schaufelberger. Block Pulse Functions and Their Applications in Control Systems. Springer, 1992.

Kanwal, Ram P. Linear Integral Equations Theory & Technique (Second Edition). Springer Science+Business Media, 1997.

Maleknejad, K., H. Almasieh and M. Roodaki. Triangular Functions (TF) Method for the Solution of Nonlinear Volterra-Fredholm Integral Equations. Communications in Nonlinear Science and Numerical Simulation, 15(11):3293-3298, 2010.

Maleknejad, K., M. Khodabin, and F. Hosseini Shekarabi. Modified Block Pulse Functions for Numerical Solution of Stochastic Volterra Integral Equations. Journal of Applied Mathematics, 4:1-10, 2014.

Nemati, S. Numerical Solution of Volterra-Fredholm Integral Equations Using Legendre Collocation Method. Journal of Computational and Applied Mathematics, 278:29-36, 2015.

Rahman, M. Integral Equations and Their Applications. WIT Press, 2007.

Tang, Xiaojun. Numerical Solution of Volterra-Fredholm Integral Equations Using Parameterized Pseudospectral Integration Matrices. Applied Mathematics and Computation, 270(1):744-755, 2015.

Wazwaz, Abdul-Majid. Linear and Nonlinear Integral Equations (Methods and Applications), Higher Education Press and Springer-Verlag Berlin Heidelberg, 2011.

Wazwaz, Abdul-Majid. A First Course in Integral Equations (Second Edition), World Scientific, 2015.

Yalcinbas, Salih. Taylor Polynomial Solutions of Nonlinear Volterra-Fredholm Integral Equations. Applied Mathematics and Computation, 127(2-3):195-206, 2002.

DOI: https://doi.org/10.24198/jmi.v17.n1.32003.33-42