Three-point Block Algorithm For Approximating Duffing Type Differential Equations

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.