A hybrid method to systems of Fredholm integral differential equations. (English) Zbl 07926993
Summary: The method used in this research consists of a hybrid of the Block-Pulse functions and third-kind Chebyshev polynomials for solving systems of Fredholm integral differential equations. Through the use of an operational matrix representing the derivation, the problem is represented by a system of algebraic equations. Some examples are provided to illustrate the simplicity and effectiveness of the utilized method. In addition, results of the presented method have been compared with those obtained from the Tau method and variational iteration method that reveal the proposed scheme to be more applicable.
MSC:
| 65R20 | Numerical methods for integral equations |
| 33C47 | Other special orthogonal polynomials and functions |
Keywords:
system of Fredholm integral differential equations; hybrid method; block-pulse functions; third-kind Chebyshev polynomials; operational matrixReferences:
| [1] | J. Biazar, H. Ebrahimi, A Strong Method for Solving System of Integral Differential Equations, Applied Mathematics, 2(9), (2011), 1105-1113. |
| [2] | A. Hosry, R. Nakad, S. Bhalekar, A Hybrid Function Approach to Solving a Class of Fred-holm and Volterra Integro-Differential Equations, Math. Comput. Appl., 25(2), (2020), 30. |
| [3] | C. Hsiao, Hybrid Function Method for Solving Fredholm and Volterra Integral Equations of the Second Kind, Journal of Computational and Applied Mathematics, 230(1), (2009), 59-68. · Zbl 1167.65473 |
| [4] | R. Jafari, R. Ezzati, K. Maleknejad, Numerical Solution of Fredholm Integro-Differential Equations By Using Hybrid Function Operational Matrix of Differentiation, Int. J. In-dustrial Mathematics, 9(4), (2017), 349-358. |
| [5] | Z. H. Jiang, W. Schaufelberger, Block-Pulse Functions and Their Applications in Control Systems, Springer-Verlag, Berlin, Heidelberg, 1992. · Zbl 0784.93004 |
| [6] | K. Maleknejad, Y. Mahmoudi, Numerical Solution of Linear Fredholm Integral Equation by Using Hybrid Taylor and Block-Pulse Functions, Appl. Math. Comput., 149, (2004), 799-806. · Zbl 1038.65147 |
| [7] | K. Maleknejad, M. Tavassoli Kajani, A Hybrid Collocation Method Based on Combining the Third Kind Chebyshev Polynomials and Block-Pulse Functions for Solving Higer-Order Initial Value Problems, Kuwait journal of Science, 43(4), (2016), 1-10. · Zbl 1463.65207 |
| [8] | J. Pour-Mahmoud, M. Y. Rahimi-Ardabili, S. Shahmorad, Numerical Solution of the System of Fredholm Integro-Differential Equations by the Tau Method, Applied Mathe-matics and Computation, 168(1), (2005), 465-478. · Zbl 1082.65600 |
| [9] | G. P. Rao, L. Sivakumar, Analysis Analysis and Synthesis of Dynamic Systems Contain-ing Time-Delays Via Block-Pulse Functions, Proc. IEE, 125, (1978), 1064-1068. |
| [10] | M. Razzaghi, Fourier Series Approach for the Solution of Linear Two-Point Boundary Value Problems with Time-Varying Coefficients, Int. J. Syst. Sci., 21(9), (1990), 1783-1794. · Zbl 0712.34015 |
| [11] | P. Sannuti, Analysis and Synthesis of Dynamic Systems Via Block-Pulse Functions, Proc. Inst. Elect. Eng., 124(6), (1977), 569-571. |
| [12] | M. Tavassoli Kajani, A. Hadi Vencheh, Solving Second Kind Integral Equations with Hybrid Chebyshev and Block-Pulse Functions, Appl. Math. Comput., 163(1), (2005), 71-77. · Zbl 1067.65151 |
| [13] | X. T. Wang, Y. M. Li, Numerical Solutions of Integro-Differential Systems by Hybrid of General Block-Pulse Functions and the Second Chebyshev Polynomials, Appl. Math. Comput., 209(2), (2009), 266-272. · Zbl 1161.65099 |
| [14] | X. T. Wang, Numerical Solutions of Optimal Control for Time Delay Systems by Hy-brid of Block-Pulse Functions and Legendre Polynomials, Appl. Math. Comput., 184(2), (2007), 849-856. · Zbl 1114.65076 |
| [15] | X. T. Wang, Numerical Solution of Time-Varying Systems with a Stretch by General Legendre Wavelets, Appl. Math.comput., 198(2), (2008), 613-620. · Zbl 1138.65056 |
| [16] | A. Wazwaz, Linear and Nonlinear Integral Equations, Methods And Applications, Springer Berlin, Heidelberg, 2011. [ Downloaded from ijmsi.ir on 2024-09-09 ] Powered by TCPDF (www.tcpdf.org) · Zbl 1227.45002 |
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