Abstract
ABSTRACTIn 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.
Highlights
Differential equation and systems are very useful materials both mathematical modelling and to find out some mathematical equations
Many scientists have been motivated that scientists have been studied many numerical methods to solve systems of differential equations such as Runga kutta method [11], DTM
Chebyshev operational method has been applied to numerically solve the systems of differential equations
Summary
Differential equation and systems are very useful materials both mathematical modelling and to find out some mathematical equations. Many problems in applied science are modelled mathematically by using a systems of ordinary differential equations, for example, pollution modelling and its numerical solutions [1], kinetic modelling of lactic acid [2], the prey and predator problem [3,4], modelling of the epidemiological model for computer viruses [5], modelling of mosquito dispersal [6], modelling a thermal explosion [7], dynamical models of happiness [8], stagnation point flow and Lorentz force [9], non-spherical particles sedimentation [10], boundary layer analysis of micropolar dusty fluid with TiO2 nanoparticles in a porous medium [11], boundary layer flow of an Eyring-Powell non-Newtonian fluid over a linear stretching sheet [12], heat transfer [13], two-phase Couette flow analysis [14] Due to these reasons, the solutions of these equations are great importance among scientists. Tn(x) The first kind Chebychev polynomials Tn∗(x) The first kind shifted Chebychev polynomials anj The unknown coefficients yNj (x) The approximate solutions N1 The absolute error
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