### Journals Information

Mathematics and Statistics Vol. 10(3), pp. 529 - 541
DOI: 10.13189/ms.2022.100308
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## Three-Point Block Algorithm for Approximating Duffing Type Differential Equations

Ahmad Fadly Nurullah Rasedee 1,*, Mohammad Hasan Abdul Sathar 2, Najwa Najib 1, Nurhidaya Mohamad Jan 3, Siti Munirah Mohd 3, Siti Nor Aini Mohd Aslam 4
1 Faculty of Economics and Muamalat, Universiti Sains Islam Malaysia, Malaysia
2 Centre of Foundation Studies for Agricultural Science, Putra University of Malaysia, Malaysia
3 Kolej Genius Insan, Universiti Sains Islam Malaysia, Malaysia
4 Mathematics Department, Kampus Dengkil, Universiti Teknologi Mara, Malaysia

ABSTRACT

The current study was conducted to establish a new numerical method for solving Duffing type differential equations. Duffing type differential equations are often linked to damping issues in physical systems, which can be found in control process problems. The proposed method is developed using a three-point block method in backward difference form, which offers an accurate approximation of Duffing type differential equations with less computational cost. Applying an Adam's like predictor-corrector formulation, the three point block method is programmed with a recursive relationship between explicit and implicit coefficients to reduce computational cost. By establishing this recursive relationship, we established a corrector algorithm in terms of the predictor. This eliminates any undesired redundancy in the calculation when obtaining the corrector. The proposed method allows a more efficient solution without any significant loss of accuracy. Four types of Duffing differential equations are selected to test the viability of the method. Numerical results will show efficiency of the three-point block method compared against conventional and more established methods. The outcome of this research is a new method for successfully solving Duffing type differential equation and other ordinary differential equations that are found in the field of science and engineering. An added advantage of the three-point block method is its adaptability to parallel programming.

KEYWORDS
ODEs, Block, Multistep Method, Variable Order Step Size

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Ahmad Fadly Nurullah Rasedee , Mohammad Hasan Abdul Sathar , Najwa Najib , Nurhidaya Mohamad Jan , Siti Munirah Mohd , Siti Nor Aini Mohd Aslam , "Three-Point Block Algorithm for Approximating Duffing Type Differential Equations," Mathematics and Statistics, Vol. 10, No. 3, pp. 529 - 541, 2022. DOI: 10.13189/ms.2022.100308.

(b). APA Format:
Ahmad Fadly Nurullah Rasedee , Mohammad Hasan Abdul Sathar , Najwa Najib , Nurhidaya Mohamad Jan , Siti Munirah Mohd , Siti Nor Aini Mohd Aslam (2022). Three-Point Block Algorithm for Approximating Duffing Type Differential Equations. Mathematics and Statistics, 10(3), 529 - 541. DOI: 10.13189/ms.2022.100308.