NUMERICAL SOLUTIONS OF SYSTEM OF FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

Abstract

Abstract Background: System of Fredholm integro-differential equations is a hot topic in applied mathematics; in particular, the field of signal processing, neural networks and the development of telecommunications. Aims: This thesis presents some numerical methods based on matrix polynomials to solve system of Fredholm integro-differential equations. These methods are: Laguerre polynomials, Bessel functions and Legendre polynomial. Methods: In this study, we use Matlab software to implement these methods in form of algorithms to solve some numerical examples. Results: Numerical results show that the convergence and accuracy proprieties of these methods are in good agreement with the exact solution. Conclusion: A comparison of numerical results illustrated in tables and figures shows that the Laguerre polynomials method provides more accurate results than the other methods and therefore more effective. Keywords: solution of system, fredholm, integro-differential, matlab, numerical methods, integrodifferential.