### Journals Information

Mathematics and Statistics Vol. 10(1), pp. 1 - 14
DOI: 10.13189/ms.2022.100101
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## Accuracy and Efficiency of Symmetrized Implicit Midpoint Rule for Solving the Water Tank System Problems

M. F. Zairul Fuaad 1, N. Razali 1,2,*, H. Hishamuddin 1, A. Jedi 1
1 Department of Mechanical and Manufacturing Engineering, Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia, Malaysia
2 Department of Engineering Education, Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia, Malaysia

ABSTRACT

The accuracy and efficiency of water tank system problems can be determined by comparing the Symmetrized Implicit Midpoint Rule (IMR) with the IMR. Static and dynamic analyses are part of a mathematical model that uses energy conservation to generate a nonlinear Ordinary Differential Equation. Static analysis provides optimal working points, while dynamic analysis outputs an overview of the system behaviour. The procedure mentioned is tested on two water tank designs, namely, cylindrical and rectangular tanks with two different parameters. The Symmetrized IMR is used in this study. Results show that the two-step active Symmetrized IMR applied on the proposed mathematical model is precise and efficient and can be used for the design of appropriate controls. The cylindrical water tank model takes the fastest time in emptying the water tank. The approach of the various water tank models shows an increase in accuracy and efficiency in the range of parameters used for practical model applications. The results of the numerical method show that the two-step Symmetrized IMR provides more precise stability, accuracy and efficiency for the fixed step size measurements compared with other numerical methods.

KEYWORDS
Water Tank, Ordinary Differences Equation, Symmetrization Implicit Midpoint Rule, Accuracy, Efficiency

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] M. F. Zairul Fuaad , N. Razali , H. Hishamuddin , A. Jedi , "Accuracy and Efficiency of Symmetrized Implicit Midpoint Rule for Solving the Water Tank System Problems," Mathematics and Statistics, Vol. 10, No. 1, pp. 1 - 14, 2022. DOI: 10.13189/ms.2022.100101.

(b). APA Format:
M. F. Zairul Fuaad , N. Razali , H. Hishamuddin , A. Jedi (2022). Accuracy and Efficiency of Symmetrized Implicit Midpoint Rule for Solving the Water Tank System Problems. Mathematics and Statistics, 10(1), 1 - 14. DOI: 10.13189/ms.2022.100101.