Symmetries of Bernstein Polynomial Differentiation Matrices and Applications to Initial Value Problems
সংরক্ষণ করুন:
| প্রকাশিত: | Symmetry vol. 17, no. 1 (2025), p. 47 |
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| প্রধান লেখক: | |
| অন্যান্য লেখক: | , , , |
| প্রকাশিত: |
MDPI AG
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| বিষয়গুলি: | |
| অনলাইন ব্যবহার করুন: | Citation/Abstract Full Text + Graphics Full Text - PDF |
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| সার সংক্ষেপ: | In this study, we discuss the symmetries underlying Bernstein polynomial differentiation matrices, as they are used in the collocation method approach to approximate solutions of initial and boundary value problems. The symmetries are brought into connection with those of the Chebyshev pseudospectral method (Chebyshev polynomial differentiation matrices). The treatment discussed here enables a faster and more accurate generation of differentiation matrices. The results are applied in numerical solutions of several initial value problems for the partial differential equation of convection–diffusion reaction type. The method described herein demonstrates the combination of advanced numerical techniques like polynomial interpolation, stability-preserving timestepping, and transformation methods to solve a challenging nonlinear PDE efficiently. The use of Bernstein polynomials offers a high degree of accuracy for spatial discretization, and the CGL nodes improve the stability of the polynomial approximation. This analysis shows that exploiting symmetry in the differentiation matrices, combined with the wise choice of collocation nodes (CGL), leads to both accurate and efficient numerical methods for solving PDEs and accuracy that approach pseudospectral methods that use well-known orthogonal polynomials such as Chebyshev polynomials. |
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| আইএসএসএন: | 2073-8994 |
| ডিওআই: | 10.3390/sym17010047 |
| সম্পদ: | Engineering Database |