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Solving third-order boundary value problems with quartic splines.

P K Pandey1

  • 1Department of Mathematics, Dyal Singh College, University of Delhi, Lodhi Road, New Delhi, 110003 India.

Springerplus
|April 12, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces a new numerical method using quartic polynomial splines for solving third order boundary value problems. The developed second order method demonstrates superior accuracy and efficiency in numerical experiments.

Keywords:
Boundary-value problemsFinite-difference methodsObstacle problemsQuartic polynomial splines

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Area of Science:

  • Numerical Analysis
  • Applied Mathematics
  • Computational Science

Background:

  • Third order boundary value problems (BVPs) are common in various scientific and engineering fields.
  • Existing numerical methods may face challenges in terms of accuracy and efficiency for these problems.

Purpose of the Study:

  • To develop and analyze a novel second order numerical method for solving third order BVPs.
  • To utilize quartic polynomial splines as the basis for the numerical approximation.

Main Methods:

  • A second order numerical scheme is constructed using quartic polynomial splines.
  • The convergence analysis of the proposed method is rigorously established.
  • Numerical experiments are conducted to validate the method's performance.

Main Results:

  • The proposed method achieves second order accuracy.
  • Numerical experiments confirm the efficiency and effectiveness of the method.
  • The quartic spline-based method provides improved results compared to existing approaches.

Conclusions:

  • The novel second order numerical method is effective for solving third order BVPs.
  • Quartic polynomial splines offer a robust framework for developing accurate numerical solutions.
  • The method's demonstrated efficiency and validity make it a valuable tool for researchers.