Direct application of Padé approximant for solving nonlinear differential equations
Hector Vazquez-Leal1, Brahim Benhammouda2, Uriel Filobello-Nino1
1Electronic Instrumentation and Atmospheric Sciences School, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, Mexico.
Springerplus
|October 22, 2014
Summary
This study introduces a direct Padé method for solving nonlinear differential equations, yielding accurate rational approximations. This approach bypasses traditional series methods, offering a more efficient way to find solutions.
Area of Science:
- Applied Mathematics
- Numerical Analysis
Background:
- Nonlinear differential equations require robust solution methods.
- Existing semi-analytical techniques often involve multiple steps or approximations.
Purpose of the Study:
- To present a direct procedure for applying the Padé method to nonlinear differential equations.
- To demonstrate the method's efficacy in generating accurate rational approximate solutions.
Main Methods:
- Direct application of the Padé method.
- Testing on nonlinear boundary value, differential-algebraic oscillator, and asymptotic problems.
Main Results:
- The direct Padé method generates highly accurate rational approximate solutions.
- The method proved effective for diverse nonlinear equation types.
- Achieved superior accuracy compared to other semi-analytical methods.
Conclusions:
- The direct Padé method is a powerful and efficient tool for approximating solutions to nonlinear differential equations.
- This approach simplifies the solution process by avoiding preliminary approximation methods like Taylor series.
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