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Laplace transform homotopy perturbation method for the approximation of variational problems.
U Filobello-Nino1, H Vazquez-Leal1, M M Rashidi2
1Facultad de Instrumentación Electrónica, Universidad Veracruzana, Circuito Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, Veracruz Mexico.
Springerplus
|March 24, 2016
Summary
This study applies the Laplace Transform-Homotopy Perturbation Method to solve differential equations from variational problems. The method demonstrates high accuracy, yielding exact solutions and confirming its effectiveness for complex problems.
Area of Science:
- Applied Mathematics
- Numerical Analysis
Background:
- Variational problems often lead to complex linear and nonlinear differential equations.
- Analytical approximate solutions are crucial for understanding and solving these equations.
Purpose of the Study:
- To apply and evaluate the Laplace Transform-Homotopy Perturbation Method (LT-HPM) and its modifications.
- To find accurate analytical approximate solutions for differential equations arising from variational problems.
Main Methods:
- The Laplace Transform-Homotopy Perturbation Method (LT-HPM).
- Application to four specific ordinary differential equations derived from variational problems.
Main Results:
- The proposed methods successfully generated analytical approximate solutions.
- High accuracy was achieved, with one case yielding an exact solution.
- The square residual error for the approximate solutions was found to be within [0.001918936920, 0.06334882582].
Conclusions:
- The LT-HPM and its modifications are effective for solving differential equations in variational problems.
- The methods provide accurate and reliable solutions, even for complex mathematical challenges.
- The low square residual error validates the precision of the proposed techniques.
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