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Parameter identification in multidimensional hyperbolic partial differential equations using wavelet collocation method
Author(s) -
Priyadarshi Gopal,
Rathish Kumar Bayya Venkatesulu
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7336
Subject(s) - mathematics , haar wavelet , wavelet , hyperbolic partial differential equation , partial differential equation , collocation method , collocation (remote sensing) , multiresolution analysis , orthogonal collocation , mathematical analysis , interpolation (computer graphics) , discrete wavelet transform , differential equation , wavelet transform , ordinary differential equation , computer science , animation , computer graphics (images) , artificial intelligence , machine learning
In this article, we have proposed a highly efficient and accurate collocation method based on Haar wavelet for the parameter identification in multidimensional hyperbolic partial differential equations (PDEs). In the proposed method, highest order derivative is represented in terms of Haar wavelet and required term of the PDE is obtained using successive integration. Due to compact support and orthogonality of Haar wavelet, this method leads to significant reduction in the computational cost. Cubic spline interpolation and Taylor series approximation are used for the parameter identification. Error analysis is carried out in order to prove the convergence of the method. The obtained numerical results and central processing unit (CPU) time ensure the efficiency and accuracy of the method.