Journal of Emerging Trends in Engineering and Applied Sciences: Research Areas

Abstract:
In this paper, a new set of family of Non-Standard finite difference schemes for the solution of combustion equation is discussed. A logical method for constructing the denominator functions for the discrete derivatives was considered and used to construct the schemes. The method of Non-Local Approximation was used to implement them. The importance of making a suitable combination of "choice of free parameters and appropriate denominator function" is explicated. The preservation of the qualitative properties of some IVPs arising from the combustion equation by these proposed schemes are discussed. Numerical experiments have been used to verify some stability properties of the new finite difference schemes proposed for the Combustion Equation.

Keywords: non-local approximations, denominator functions (type a and b), modeling, non-standard method, qualitative properties, ivp (initial value problem), combustion equation

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