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Analytical solutions for systems of partial differential-algebraic equations
Brahim Benhammouda1, Hector Vazquez-Leal2
1Higher Colleges of Technology, Abu Dhabi Men's College, P.O. Box 25035, Abu Dhabi, United Arab Emirates.
Springerplus
|April 18, 2014
Summary
The power series method (PSM) offers analytical solutions for partial differential-algebraic equations (PDAEs). Combining PSM with Laplace-Padé resummation provides exact solutions without secular terms or perturbation parameters.
Area of Science:
- Numerical Analysis
- Applied Mathematics
- Differential Equations
Background:
- Partial differential-algebraic equations (PDAEs) are complex systems requiring robust solution methods.
- Existing methods may involve approximations or limitations like secular terms.
Purpose of the Study:
- To apply the power series method (PSM) for solving PDAEs.
- To demonstrate PSM's capability in generating analytical solutions in convergent series form.
- To enhance solutions using the Laplace-Padé (LP) resummation method.
Main Methods:
- Application of the power series method (PSM) to PDAEs.
- Solving index-one and index-three PDAE systems.
- Post-treatment of power series solutions with Laplace-Padé (LP) resummation.
Main Results:
- PSM successfully provided analytical solutions for PDAEs in convergent series.
- The Laplace-Padé (LP) method effectively transformed series solutions into exact solutions.
- The methodology is straightforward, avoiding secular terms and perturbation parameters.
Conclusions:
- PSM is a viable and effective technique for solving PDAEs.
- The combination of PSM and LP resummation offers a powerful strategy for obtaining exact solutions.
- This approach simplifies the solution process for complex PDAE systems.
Keywords:
Laplace transformPadé approximant; Analytical solutionsPartial differential-algebraic equationsPower series methodMore Related Videos
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