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Analytical approximate solutions for a general class of nonlinear delay differential equations
Bogdan Căruntu1, Constantin Bota1
1Department of Mathematics, "Politehnica" University of Timişoara, Piaţa Victoriei 2, 300006 Timişoara, Romania.
Thescientificworldjournal
|August 26, 2014
Summary
The polynomial least squares method (PLSM) provides accurate analytical solutions for nonlinear delay differential equations. This approach is effective for complex models in areas like biology and physics.
Area of Science:
- Mathematics
- Applied Mathematics
- Numerical Analysis
Background:
- Strongly nonlinear delay differential equations (DDEs) present significant analytical challenges.
- Existing methods for solving DDEs may have limitations in accuracy or generality.
- Approximate solutions are crucial for understanding complex dynamical systems described by DDEs.
Purpose of the Study:
- To introduce and validate the polynomial least squares method (PLSM) for solving a broad range of nonlinear DDEs.
- To demonstrate the applicability of PLSM to specific problems, including pantograph equations and biological models.
- To assess the accuracy and efficiency of PLSM compared to established numerical techniques.
Main Methods:
- The polynomial least squares method (PLSM) is employed to derive analytical approximate polynomial solutions.
- PLSM is applied to solve various strongly nonlinear delay differential equations.
- Solutions obtained via PLSM are compared against previously published results from alternative methods.
Main Results:
- PLSM successfully generates analytical approximate polynomial solutions for general nonlinear DDEs.
- The method shows effectiveness when applied to pantograph equations and a biological time-delay model.
- Accuracy comparisons confirm the reliability of PLSM, often outperforming other techniques.
Conclusions:
- The polynomial least squares method (PLSM) is a powerful and versatile tool for approximating solutions to nonlinear DDEs.
- PLSM offers a robust alternative for analyzing complex systems in mathematics, physics, and biology.
- The method's accuracy and general applicability make it valuable for scientific research.
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