Different Mathematical Models

There are different mathematical models developed and used to get insight into different situations. Mathematical models can take different forms such as differential equations and statistical models. Mathematical models are abstractions of reality. The models are used to represent particular situations or ideas. Mathematical models are simplified representation of real entities in the world. The models can be equations and computer codes. Mathematical models have limitations which affect their usefulness in forecasting. They are abstraction of reality. Mathematical modeling involves a tradeoff between three things. That is generality, precision and realism. The worth of the model depends on the goals of the person modeling the model. The modelers might not include realism, generality and precision in their models. The decision to include realism, precision and generality depends on the goal. Therefore, the modeler has to sacrifice reality, precision or generality. The complexity of mathematical models entails tradeoff between their accuracy and simplicity. The simple models are more desirable unlike those with equal predictive power. Though adding complexity enhances the model realism, it has a negative effect. It makes the model hard to comprehend and evaluate. It also results to computational issues. This affects analysis of problems in the world as the information provided is not accurate. Modelers find it hard to analyze the numerical data and thus provide poor results (Bender, 2000).

Though mathematical models have disadvantages, they have advantages. Mathematical models are important in forecasting and analysis of real life situations as they have various advantages. Mathematical models help in understanding parameters and effective. Mathematical modeling involves modeling of different variables and parameters. The parameters and variables are modeled to show a relationship between them. Using theories and other methods to show the relationship between the parameters and variables might not be effective. This is because the theories do not offer comprehensive information about the parameters and their relationship. An excellent mathematical model offers a common framework for comprehending what may otherwise appear to be different and unrelated phenomena (Bender, 2000). Mathematical models are useful in developing and resting theories. They are also useful in evaluating quantitative conjures and answering certain questions. Further, mathematical models help determine change in values of parameters used and estimate values from data (Kapur, 1988).

Conceptual modeling is the abstract depiction of a problem domain. Conceptual modeling helps understand compound problem domains. A good conceptual model is not supposed to mirror a solution bias. A conceptual model should not model the solution domain, but the problem domain. However, the conceptual models might not model the problem domain, but the solution domain. This results to bias. Most of the abstract models utilized in forecasting are simple, and this makes it hard to represent real entities in the world. The abstract models cannot represent the real entities in the world due to the complexity of the real world. The difference between the complexity of the real world and simplicity of the forecasting models has affected forecasting negatively. This is because the models do not provide accurate information. Therefore, modelers should be careful when using mathematical models during forecasting. Adding complexity to the model affects the model and leads to numerical analysis problem (Thalheim, Kangassalu, Akoka & et al, 1999).

Reference

Bender, E.A. (2000). An introduction to mathematical modeling. Courier Dover publication

Kapur, J.N. (1988). Mathematical modeling. New Age international

Thalheim, B., Kangassalu, H., Akoka, J., & et al. (1999). Conceptual modeling. Springer

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