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The Bernoulli wavelets operational matrix of integration and its applications for the solution of linear and nonlinear problems in calculus of variations

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  • Keshavarz, E.
  • Ordokhani, Y.
  • Razzaghi, M.

Abstract

In this paper, a new method for solving some classes of linear and nonlinear problems in calculus of variations is presented. The method is based upon Bernoulli wavelets. The operational matrices of integration and product of Bernoulli wavelets are calculated. These matrices are then utilized to reduce the calculus of variations problems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Suggested Citation

  • Keshavarz, E. & Ordokhani, Y. & Razzaghi, M., 2019. "The Bernoulli wavelets operational matrix of integration and its applications for the solution of linear and nonlinear problems in calculus of variations," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 83-98.
    • Handle: RePEc:eee:apmaco:v:351:y:2019:i:c:p:83-98
    DOI: 10.1016/j.amc.2018.12.032
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    References listed on IDEAS

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    1. N. Haddadi & Y. Ordokhani & M. Razzaghi, 2012. "Optimal Control of Delay Systems by Using a Hybrid Functions Approximation," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 338-356, May.
    2. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
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    Cited by:

    1. Faheem, Mo & Raza, Akmal & Khan, Arshad, 2021. "Collocation methods based on Gegenbauer and Bernoulli wavelets for solving neutral delay differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 72-92.

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