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Nonlinearities distribution Laplace transform-homotopy perturbation method
Uriel Filobello-Nino1, Hector Vazquez-Leal1, Brahim Benhammouda2
1Electronic Instrumentation and Atmospheric Sciences School, Universidad Veracruzana, Circuito Gonzalo Aguirre Beltrán S/N, Xalapa, 9100 Veracruz México.
Springerplus
|November 14, 2014
Summary
This study introduces the non-linearities distribution Laplace transform-homotopy perturbation method (NDLT-HPM) for solving differential equations. The NDLT-HPM effectively handles complex equations, demonstrating its utility in finding approximate solutions.
Area of Science:
- Applied Mathematics
- Numerical Analysis
Background:
- Differential equations are fundamental in modeling various scientific phenomena.
- Solving complex nonlinear differential equations with non-polynomial terms remains a challenge.
Purpose of the Study:
- To propose and validate a novel analytical method for solving differential equations.
- To address equations with nonhomogeneous and non-polynomial terms.
Main Methods:
- The study employs the non-linearities distribution Laplace transform-homotopy perturbation method (NDLT-HPM).
- This method combines Laplace transforms and the homotopy perturbation technique.
Main Results:
- The NDLT-HPM provides approximate solutions for linear and nonlinear differential equations.
- The method shows particular effectiveness for equations with nonhomogeneous, non-polynomial terms.
- Comparisons with exact solutions confirm the method's accuracy.
Conclusions:
- The NDLT-HPM is an effective technique for solving a range of differential equations.
- The proposed method offers a reliable approach for complex mathematical models.
Keywords:
Approximate solutionsFinite boundary conditionsHomotopy perturbation methodLaplace transformLaplace transform homotopy perturbation methodNonlinear differential equationMore Related Videos
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