This paper concerns the implementation of the orthogonal polynomials using the Galerkin method for solving Volterra integro-differential and Fredholm integro-differential equations. The constructed orthogonal polynomials are used as basis functions in the assumed solution employed. Numerical examples for some selected problems are provided and the results obtained show that the Galerkin method with orthogonal polynomials as basis functions performed creditably well in terms of absolute errors obtained.
References
[1]
Atkinson, K. (1997) Numerical Solution of Integral Equation of the Second Kind. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511626340
[2]
Venkatesh, S.G., Ayyaswamy, S.K. and Raja Balachandar, S. (2012) Legendre Approximation Solution for a Class of Higher-Order Volterra Integro-Differntial Equations. Ain Shams Engineering Journal, 3, 417-422. https://doi.org/10.1016/j.asej.2012.04.007
[3]
Dehghan, M. and Shakeri, F. (2008) Solution of an Integro-Differential Arising in Oscillating Magnetic Field Using Homotopy Perturbation Method. Progressive in Electromagnetic Research, 78, 361-376. https://doi.org/10.2528/PIER07090403
[4]
Jangveladze, T., Kiguradz, Z. and Neto, B. (2011) Galerkin Finite Element Method for One Non-Linear Integro-Differential Model. Applied Mathematics and Computation, 217, 6883-6892. https://doi.org/10.1016/j.amc.2011.01.053
[5]
Maleknejad, K. and Tavassoli-Kajani, M. (2011) Solving Linear Integro-Differential Equations System by Galerkin Method with Hybrid Functions. Applied Mathematics and Computation, 150, 603-612. https://doi.org/10.1016/j.amc.2003.10.046
[6]
Ghasemi, T., Tavassol-Kajani, M. and Babolian, E. (2007) Numerical Solution of Nonlinear Integro-Differential Equations. Wave-Galerkin Method and Homotopy Perturbation Method. Applied Mathematics and Computation, 188, 450-455. https://doi.org/10.1016/j.amc.2006.10.001
[7]
Fakhar-Izadi, F. and Dehghan, M. (2011) An Efficient Pseudo-Spectral Legendre Galarkin Method for Solving a Nonlinear Integro-Differetial Equations Arising in Population Dynamics. Mathematical Method for Applied Sciences, 30, 1485-1511. https://doi.org/10.1002/mma.2698
[8]
Tomassiello, S.A. (2011) A Note on Three Numerical Procedures to Solve Volterra Integro-Differential Equations on Structural Analysis. Applied Mathematics and Computation, 62, 3188-3193. https://doi.org/10.1016/j.camwa.2011.08.031
