A Fourth-Order Compact Finite Difference–Boole’s Method for Solving Linear Integro-Differential Equations

Authors

  • Samuel Terungwa Gbanor University of Africa Toru-Orua, Bayelsa State.

DOI:

https://doi.org/10.63561/jmns.v2i4.1124

Keywords:

Absolute, Error, Boole’s rule, CFDM, LIDEs

Abstract

In this paper, the fourth order Compact Finite Difference – Boole’s Method was used to solve linear Integro-differential equations of first and second orders respectively. The discretized unknown function in each case formed a system of linear algebraic equations and was subsequently solved using MATLAB package. The approximate solutions arrived at  from the combined method have been compared with exact and other existing solutions of the given numerical problems which show that the proposed method is very e asy, powerful and efficient in determining approximate solutions to linear integro-differential equations.

References

Second Kind. American Journal of Computational Mathematics, 7(02), 157-165.

Atkinson K. (1997). The Numerical Solution of Integral Equations of the Second Kind, Cambridge University press.

Auchunan E., & Sulaiman J. (2011)Half-sweep Conjugate Gradient Method for solving First Order Linear Fredholm Integro-differential Equations. Australian Journal of Basic and Applied Sciences, 5(3):38-43,2011. ISSN 1991-8178.

Aziz, I. & Ain Q.U. (2020) Numerical solution of partial Integro-differential equations with weakly singular kernel. Advanced Mathehematical models and applications.5(149),60.

Bashir D. G. & Sirajo L.B. (2021). A hybrid method for solution of linear Volterra integro-differential equations (LVIDES) via finite difference and Simpson’s numerical methods (FDSM).Journal of Mathematical Analysis (OMA).Volume 5 (2021) Issue 1Pages: 69- 75.ISSN: 2616-8111 (Online) 2616-8103(Print). DOI: https://www.doi.org/10.30538/psrp-oma2021.0084.

Chen, H., & Zhang, C. (2011). Boundary value methods for Volterra integral and integro-differential equations. Applied Mathematics and Computation, 218(6), 2619-2630.

Darania, P., & Ebadian, A. (2007). A method for the numerical solution of the integro- differential equations. Applied Mathematics and Computation, 188(1),657-668.

Elahi Z. , Akram G., Siddiqi S.S. (2018) Laguerre approach for solving systems of linear Fredholm Integro-differential Equations. Differ Math Sdenc. (2018) 10.1007/s40096-018-0258-0

Garba, B. D., & Bichi, S. L. (2020). On solving linear Fredholm integro-differential equations via finite difference-Simpson’s approach. Malaya Journal of Matematik (MJM), 8(2), 469-472.

Heris, J. M. (2012). Solving the integro-differential equations using the modified Laplace Adomian decomposition method. Journal of Mathematical Extension, 6(1), 41-55.

Kurt, N., & Sezer, M. (2008). Polynomial solution of high-order linear Fredholm. Integro-differential equations with constant coefficients. Journal of the Franklin Institute, 345(8), 839-850.

Mirzaee F., & Hoseini S.S.(2017). A new collocation Approch for solving systems of high order linear Volterra Integro-differential Equations with variable coefficient. Appl. Math. Comput, 311(2017), pp272-282.

Saadati, R., Raftari, B., Abibi, H., Vaezpour, S. M., & Shakeri, S. (2008).Comparison between the Variational Iteration method and Trapezoidal rule solving linear integro-differential equations. World Applied Sciences Journal 4(3), 321-325.

Sahu P.K., & Saha, R.S. (2015). Legendre wavelets operational method for the Numerical solution of non linear volterra integro-differential equations systems.Appl Math Comput, 256(2015), pp 715-723.

Sameeh, M. & Elsaid, A. (2016). Chebyshev collocation method for parabolic Partial integro-differential Equations. Advances in Mathematical Physics. 2016(1-7).

Solimam A.F. & EL-Azab, M.S. (2012). Compact Finite Difference Schemesfor Partial Integro-differential Equations. American Academic and Scholarly Research Journal. 4(1):6-13.

Solimam A.F., El-Asyed, A.M.A. & EL-Azab, M.S., (2012). Compact Finite Difference Schemes for solving a Class of weakly –singular Partial Integro- differential Equations. Mathematical Sciences Letters. 1(1),53-60.

Taiwo O. A. & Jimoh A. K. (2014). Comparison of some Numerical Methods for The Solution of First and Second Orders Linear Integro-differential Equations. American Journal of Engineering Research (AJER) 03 (01), 245-250.

Zhao J. (2007). Highly accurate compact mixed methods for two point boundary value problems, Appl. Math. Comput. 188 (2007),1402–1418.

Zhao J. & Coreless, R.M. (2006). Compact Finite Difference Method for Integro-differential Equations. Applied Mathematics and Computation.177(1),271-288.

Downloads

Published

2025-12-30

How to Cite

Gbanor, S. T. (2025). A Fourth-Order Compact Finite Difference–Boole’s Method for Solving Linear Integro-Differential Equations. Faculty of Natural and Applied Sciences Journal of Mathematical Modeling and Numerical Simulation, 2(4), 61–68. https://doi.org/10.63561/jmns.v2i4.1124