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Optimal control is a very significant field of modern control theory which has been applied in many areas like medicine, science, and finance. This work is based on realization of asset values as a benefit of asset management where a capital asset management problem is modelled and expressed mathematically from the perspective of an investor whose income is generated by return and capital gains on investments with price and return on assets assumed to satisfy uncertainty process. This results in an optimal control model based on uncertainty theory which relates two or more parameters that measures the condition or state of individual's investments. These parameters enable us to know the condition of risk involved in asset management and how to maintain and manage the assets in order to maximize expected present value of the utility of asset and minimize the risk involved to aid capital investment decision-making. Parameter sensitivity analysis is an approach given to a model so as to define significance of the factors related to the model where the whole parameter space is fully described. However, the model is applied to a real-life problem of capital asset management to deal with debt crisis of a nation's economy and the sensitivity analysis to determine the effects of the input factors on the model is investigated such that relative significance and sensitivity of each parameter on the model results are presented using parameter estimations. Finally the optimal control decision policy is obtained and discussed.

Abstract:To evaluate the environmental impact of pollution, mathematical models play a major role in predicting the pollution level in the regions under consideration. This paper examines the various mathematical models involving water pollutant. We also give the implicit central difference scheme in space, and a forward difference method in time for the evaluation of the generalized transport equation.

SUMMARYCubic basis functions in one dimension for the solution of two-point boundary value problems are constructed based on the zeros of Chebyshev polynomials of the first kind. A general formula is derived for the construction of polynomial basis functions of degree r, where 1 Qr< co. A Galerkin finite element method using the constructed basis functions for the cases r = 1,2 and 3 is successfully applied to three different types of problem including a singular perturbation problem.

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