Shreekant Pathak
- Assistant Professor Department of Applied Sciences and Humanities, M. B. Institute of Technology, New Vallabh Vidyanagar, Gujarat India
Abstract
In this article, we have used the Optimal Homotopy Analysis Method (OHAM), which is a basically semi-analytic method to solve differential equations. The ability for the user to choose the convergence control parameter, auxiliary linear operator, auxiliary function, and starting approximation is what sets apart the OHAM technique. We guaranteed the efficacy and efficiency of the procedure by fine-tuning the convergence control parameter. We solved a non-linear partial differential equation (PDE) using OHAM to show off its capabilities, and we verified that the series solution converged. Optimal homotopy analysis technique each person has complete discretion over selecting the auxiliary function, auxiliary linear operator, convergence control value, and beginning approximation. We use a non-linear partial differential equation (PDE) to demonstrate the power of OHAM. We guarantee the reliability and quick convergence of the series solution obtained from OHAM by carefully adjusting the convergence control parameter. Our findings confirm that the approach can yield precise and convergent solutions. Because the user may adjust the auxiliary function, linear operator, convergence parameter, and initial guess, OHAM offers a unique benefit that allows the method to be specifically tailored to the features of the differential equation being solved. In this method, we have optimized the convergence control parameter. Also we have compare the obtained result with the exact solution to check the efficiency of the method. With the assurance of the series solution’s convergence, we used this method to solve non-linear partial differential equations (PDEs).
Keywords: OHAM, PDE, Series solution, Maclaurin series, Convergence Control Paramete, Square Residual Error.
[This article belongs to Research & Reviews: Discrete Mathematical Structures(rrdms)]
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Research & Reviews: Discrete Mathematical Structures
| Volume | 11 |
| Issue | 01 |
| Received | February 7, 2024 |
| Accepted | July 12, 2024 |
| Published | July 16, 2024 |
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