Numerical solution of systems of differential equations using operational matrix method with Chebyshev polynomials

In this study, we introduce an effective and successful numerical algorithm to get numerical solutions of the system of differential equations. The method includes operational matrix method and truncated Chebyshev series which represents an exact solution. The method reduces the given problem to a set of algebraic equations including Chebyshev coefficients. Some numerical examples are given to demonstrate the validity and applicability of the method. In Examples, we give some comparison between present method and other numerical methods. The obtained numerical results reveal that given method very good approximation than other methods. Moreover, the modelling of spreading of a non-fatal disease in a population is numerically solved. All examples run the mathematical programme Maple 13.