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AIMS Mathematics

2022, Volume 7, Issue 3: 3277-3289. doi: 10.3934/math.2022182
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A new algorithm based on compressed Legendre polynomials for solving boundary value problems

  • Zhuhai Campus, Beijing Institute of Technology, Zhuhai 519088, China
  • Received: 21 September 2021 Accepted: 18 November 2021 Published: 29 November 2021

  • MSC : 65L05, 65L10

  • In this paper, we discuss a novel numerical algorithm for solving boundary value problems. We introduce an orthonormal basis generated from compressed Legendre polynomials. This basis can avoid Runge phenomenon caused by high-order polynomial approximation. Based on the new basis, a numerical algorithm of two-point boundary value problems is established. The convergence and stability of the method are proved. The whole analysis is also applicable to higher order equations or equations with more complex boundary conditions. Four numerical examples are tested to illustrate the accuracy and efficiency of the algorithm. The results show that our algorithm have higher accuracy for solving linear and nonlinear problems.

    Citation: Hui Zhu, Liangcai Mei, Yingzhen Lin. A new algorithm based on compressed Legendre polynomials for solving boundary value problems[J]. AIMS Mathematics, 2022, 7(3): 3277-3289. doi: 10.3934/math.2022182

    Related Papers:

  • In this paper, we discuss a novel numerical algorithm for solving boundary value problems. We introduce an orthonormal basis generated from compressed Legendre polynomials. This basis can avoid Runge phenomenon caused by high-order polynomial approximation. Based on the new basis, a numerical algorithm of two-point boundary value problems is established. The convergence and stability of the method are proved. The whole analysis is also applicable to higher order equations or equations with more complex boundary conditions. Four numerical examples are tested to illustrate the accuracy and efficiency of the algorithm. The results show that our algorithm have higher accuracy for solving linear and nonlinear problems.


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