On the Derivatives of Bernstein Polynomials: An Application for the Solution of High Even-Order Differential Equations

By Eid H. Doha, Ali H. Bhrawy, M. A. Saker. 2011

89 citations recorded by the source corpus.

A new formula expressing explicitly the derivatives of Bernstein polynomials of any degree and for any order in terms of Bernstein polynomials themselves is proved, and a formula expressing the Bernstein coefficients of the general-order derivative of a differentiable function in terms of its Bernstein coefficients is deduced. An application of how to use Bernstein polynomials for solving high even-order differential equations by Bernstein Galerkin and Bernstein Petrov-Galerkin methods is described. These two methods are then tested on examples and compared with other methods. It is shown that the presented methods yield better results.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7640757a1aaed886dbfd02937d3708a21434a5a5

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In Applied Mathematics

  1. Ali H. Bhrawy
  2. J. Machado
  3. Taha M. Taha
  4. M. A. Zaky
  5. Dumitru Băleanu

In Modeling and Simulation

  1. J. Machado
  2. Ali H. Bhrawy
  3. Taha M. Taha
  4. M. A. Zaky
  5. Dumitru Băleanu
  6. Xiao-jun Yang
  7. Eid H. Doha
  8. S. Ezz‐Eldien

In Numerical Analysis

  1. Ali H. Bhrawy
  2. J. Machado
  3. Taha M. Taha
  4. Dumitru Băleanu
  5. M. A. Zaky
  6. Xiao-jun Yang
  7. Eid H. Doha
  8. Waleed Mohamed Abd-Elhameed

Citations in the corpus