Numerical Solution of Linear Integral Equations Using Modified Block Pulse Functions
Keywords:
Brownian Motion, Integration Operational Matrix, Linear Integral Equations, εMBPFsAbstract
A computational method based on modified block pulse functions is proposed for solving numerically the linear Volterra and Fredholm integral equations. We obtain integration operational matrix of modified block pulse functions on interval .A modified 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 and Fredholm integral equations.Furthermore, the rate of convergence is and error analysis of the proposed method are investigated. The results show that the approximate solutions have a good of efficiency and accuracy.
References
Jiang, Z. H. and W. Schaufelberger. 1992. Block Pulse Functions and Their Applications in Control Systems. Springer, Germany.
Khodabin, M., K. Maleknejad, M. Rostami, and M. Nouri. 2012. Numerical Approach for Solving Stochastic Volterra-Fredholm Integral Equations by Stochastic Operational Matrix. Computers and Mathematics with Applications 64: 1903-1913.
Maleknejad, K. and B. Rahimi. 2011. Modification of Block Pulse Functions and Their Application to Solve Numerically Volterra Integral Equation of The First Kind. Commun Nonlinear Sci Numer Simulat 16: 2469-2477.
Maleknejad, K. and Mahmoudi Y. 2004. Numerical Solution of Linear Fredholm Integral Equations by Using Hybrid Taylor and Block Pulse Functions. Appl Math Comput 149: 799-806.
Maleknejad, K., M. Khodabin, and F. Hosseini Shekarabi. 2014. Modified Block Pulse Functions for Numerical Solution of Stochastic Volterra Integral Equations. Journal of Applied Mathematics 4: 1-10.
Maleknejad, K., Sohrabi S., and Baranji B. 2010. Application of 2D-BPFs to Nonlinear Integral Equations. Commun Nonlinear Sci Numer Simulat 15: 527-535.
Mirzaee, Farshid. 2016. Numerical Solution of System of Linear Integral Equations Via Improvement of Block-Pulse Functions. Journal of Mathematical Modeling 4(2): 133-159.
Khodabin, M., K. Maleknejad, M. Rostami, and M. Nouri. 2012. Numerical Approach for Solving Stochastic Volterra-Fredholm Integral Equations by Stochastic Operational Matrix. Computers and Mathematics with Applications 64: 1903-1913.
Maleknejad, K. and B. Rahimi. 2011. Modification of Block Pulse Functions and Their Application to Solve Numerically Volterra Integral Equation of The First Kind. Commun Nonlinear Sci Numer Simulat 16: 2469-2477.
Maleknejad, K. and Mahmoudi Y. 2004. Numerical Solution of Linear Fredholm Integral Equations by Using Hybrid Taylor and Block Pulse Functions. Appl Math Comput 149: 799-806.
Maleknejad, K., M. Khodabin, and F. Hosseini Shekarabi. 2014. Modified Block Pulse Functions for Numerical Solution of Stochastic Volterra Integral Equations. Journal of Applied Mathematics 4: 1-10.
Maleknejad, K., Sohrabi S., and Baranji B. 2010. Application of 2D-BPFs to Nonlinear Integral Equations. Commun Nonlinear Sci Numer Simulat 15: 527-535.
Mirzaee, Farshid. 2016. Numerical Solution of System of Linear Integral Equations Via Improvement of Block-Pulse Functions. Journal of Mathematical Modeling 4(2): 133-159.
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Published
2022-02-22
How to Cite
Ahmad, A. . (2022). Numerical Solution of Linear Integral Equations Using Modified Block Pulse Functions. Proceeding International Conference on Religion, Science and Education, 1, 495–500. Retrieved from http://sunankalijaga.org/prosiding/index.php/icrse/article/view/828
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